Engineering Modeling, Analysis and Optimal Design of ...

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9-2011

Engineering Modeling, Analysis and Optimal Design of Custom Engineering Modeling, Analysis and Optimal Design of Custom

Foot Orthotic Foot Orthotic

Lieselle Enid Trinidad University of Massachusetts Amherst

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ENGINEERING MODELING, ANALYSIS AND OPTIMAL DESIGN OF

CUSTOM FOOT ORTHOTIC

A Dissertation Presented

by

LIESELLE E. TRINIDAD

Submitted to the Graduate School of the

University of Massachusetts Amherst in fulfillment

of the requirements for the degree of

DOCTOR OF PHILOSOPHY

September 2011

Mechanical Engineering



A Dissertation Presented

by

Lieselle E. Trinidad

Approved as to style and content by:

_______________________________________

Professor Sundar Krishnamurty, Chair

_______________________________________

Professor Ian Grosse, Member

_______________________________________

Professor Joseph Hamill, Member

____________________________________

Professor Donald Fisher, Department Head

Mechanical & Industrial Engineering

Department

DEDICATION

This dissertation is dedicated to my parents Juan and America Trinidad, without

their endless support I would have never been able to finish. Thank You!

v

ACKNOWLEDGMENTS

I would like to acknowledge my committee Dr.’s Sundar Krishnamurty, Ian Grosse and

Joseph Hamill for guiding me through this process. Dr. Krishnamurty, you supported me

for the past 7 years in my quest for “my own research project” I know that a large portion

of this research was not in your area of interest, I thank you for sticking with me. Dr.

Grosse, thank you for your assistance with the advanced knowledge on finite element

analysis which allowed me to proceed with this research. His acceptance to serve as my

committee member is highly appreciated. Dr. Hamill, you were always so warm, open

and willing to help me in any aspect of my research, even if it wasn’t your specialty. You

gave me great advice on how to proceed and where to look for answers, thank you!

Dr. Sandra Petersen, you were always there to support me in every aspect of my

graduate career ensuring that I progressed and that I was able to succeed in finishing my

dissertation. Our mutual mentoring sessions were invaluable.

I would also like to thank my friends and labmates for their support and

constantly finding a way to keep a smile on my face, Each of you always found a way to

keep things light when tensions were high. Jay Breindel, Sarah Wood, Andrew LaPre,

Michael Berthaume, Brianna Tomboulian, and in particular Christine Dzailo and Krishna

Samavedan. I would also like to thank my older labmates from my earlier years in grad

school Tiefu Shao, Paul Witherell, Brian Mullen , Justin Rockwell. From the kinesiology

department, my other department, I would like to thank in particular Dr. Ryan Chang, Dr.

Graham Caldwell, Dr. Sandy Whittlesey, Damien Callahan, Rebecca Hasson and

Catherine Gariepy. For my friends I would like to specifically thank Shelly Perdomo,

Millicent Jackson, Caryl Ann Becerra, Mckinley Milton, Radameris Gomez, Kyle

Morrison, Laura Hutchinson, Meaghan Germain, Khadine Higgins, Allison Guley,

Darlan Harris and Yvette Quinteros Dr. Vanessa Rivera, Jaime Chernoff and Dr.Ticora

Jones.

My coaches Krista shaus, Renee Willis and Gino Arcaro, having all of you to

manage my physical and mental helth over the last two years of this process has been the

last piece to put this puzzle together. Gino I know I only met you in the last month of

this process, but your words are what powered me through the finish line.

And finally I could not have done any of this without the support of my family, in

particular my father Juan Trinidad, my mother America Trinidad, my older sister Lenina

Trinidad and her husband Steve Kenny, my younger sister Ayla, My uncle and Godfather

Jose Acevedo and my Aunt Angela Trinidad. I would also like to thank my aunt and

Godmother Maria Trinidad, my aunt Milagros Castro, and the rest of my tribe of aunts,

uncles, cousins and grandparents.

vi

ABSTRACT



September 2011

LIESELLE E. TRINIDAD, B.S., S.U.N.Y. BUFFALO

M.S.M.E, UNIVERSITY OF MASSACHUSETTS AMHERST

Ph.D., UNIVERSITY OF MASSACHUSETTS AMHERST

Directed by: Professor Sundar Krishnamurty

This research details a procedure for the systematic design of custom foot

orthotics based on simulation models and their validation through experimental and

clinical studies. These models may ultimately be able to replace the use of empirical

tables for designing custom foot orthotics and enable optimal design thicknesses based on

the body weight and activities of end-users. Similarly, they may facilitate effortless

simulation of various orthotic and loading conditions, changes in material properties, and

foot deformities by simply altering model parameters. Finally, these models and the

corresponding results may also form the basis for subsequent design of a new generation

of custom foot orthotics.

Two studies were carried out, the first involving a methodical approach to

development of engineering analysis models using the FEA technique. Subsequently, for

model verification and validation purposes, detailed investigations were executed through

experimental and clinical studies. The results were within 15% difference for the

experimental studies and 26% for the clinical studies, and most of the probability values

were greater than α = 0.05 accepting our null hypothesis that the FEA model data versus

vii

clinical trial data are not significantly different. The accuracy of the FEA model was

further enhanced when the uniform loading condition was replaced with a more realistic

pressure distribution of 70% of the weight in the heel and the rest in the front portion of

the orthotic. This alteration brought the values down to within 22% difference of the

clinical studies, with the P-values once again showed no significant difference between

the modified FEA model and the clinical studies for most of the scenarios.

The second study dealt with the development of surrogate models from FEA

results, which can then be used in lieu of the computationally intensive FEA-based

analysis models in the engineering design of CFO. Four techniques were studied,

including the second-order polynomial response surface, Kriging, non-parametric

regression and neural networking. All four techniques were found to be computationally

efficient with an average of over 200% savings in time, and the Kriging technique was

found to be the most accurate with an average % difference of below 0.30 for each of the

loading conditions (light, medium and heavy).

The two studies clearly indicate that engineering modeling, analysis and design

using FEA techniques coupled with surrogate modeling methods offer a consistent,

accurate and reliable alternative to empirical clinical studies. This powerful alternative

simulation-based design framework can be a viable and valuable tool in the custom

design of orthotics based on an individual’s unique needs and foot characteristics. With

these capabilities, the CFO prescriber would be able to design and develop the best-fit

CFO with the optimal design characteristics for each individual customer without relying

upon extensive and expensive trial and error ad hoc approaches. Such a model could also

facilitate the inspection of robustness of resulting designs, as well as enable visual

viii

inspection of the impact of even small changes on the overall performance of the CFO.

By adding the results from these studies to the CFO community, the prescription

process may become more efficient and therefore more affordable and accessible to

all populations and groups.

ix

TABLE OF CONTENTS

Page

ACKNOWLEDGMENTS ...................................................................................................v

ABSTRACT ....................................................................................................................... vi

LIST OF TABLES ............................................................................................................ xii

LIST OF FIGURES ......................................................................................................... xiv

CHAPTER

1. INTRODUCTION ...................................................................................................1

Statement of the Problem .........................................................................................6 Specific Aims ...........................................................................................................6

Study 1 .........................................................................................................6

Specific Aims #1: .............................................................................6

Study 2 .........................................................................................................8

Specific Aims #2: .............................................................................8

Significance of the studies .......................................................................................8 Summary ..................................................................................................................9 Previous work ........................................................................................................10

FEA model of a Custom Foot Orthotic ..........................................10

Introduction ........................................................................10

Methods..............................................................................11 2. LITERATURE REVIEW ......................................................................................15

Introduction ............................................................................................................15

Orthotics .................................................................................................................15

Orthotics & Finite Element ........................................................................17

Ankle Foot Orthotic Finite Element Analysis Research ............................18 Accommodative Orthotic Finite Element Analysis Research ...................19 State of the Art ...........................................................................................22

Metamodeling ........................................................................................................22

x

Summary ................................................................................................................24

3. METHODOLOGY ................................................................................................26

General Introduction ..............................................................................................26 Study 1 ...................................................................................................................26

Introduction ................................................................................................26 Verification and Validation........................................................................27

Experimental set-up and stress analysis .........................................27 Clinical trial and data collection ....................................................28

Subjects ..............................................................................31 Experimental set-up ...........................................................31

Data reduction ....................................................................32

Cantilever beam test .......................................................................32 Varying load location and arch height ...........................................34

Summary ....................................................................................................35

Study 2 ...................................................................................................................35

Introduction ................................................................................................35 Experimental set-up ...................................................................................36

Validation ...................................................................................................37

Model Building: .............................................................................38

Summary ....................................................................................................39

Summary ................................................................................................................40

4. RESULTS ..............................................................................................................41

Study I ........................................................................................................41

Instron Verification ........................................................................41

Clinical Validation .........................................................................43

Uniform Surface load .........................................................43 Varying distribution load ...................................................44

xi

Study II.......................................................................................................47

Model Validation: ..........................................................................54

5. DISCUSSION & CONCLUSIONS .......................................................................60

Study I ....................................................................................................................60

Conclusion .....................................................................................65

Case study: varying arch height and load location ....................................66

Study II...................................................................................................................69

Case study: Force load distribution using surrogate modeling ..................72

6. SUMMARY & FUTURE WORK .........................................................................81

Summary ................................................................................................................81

Future work ............................................................................................................82

APPENDIX: CLINICAL TRIAL DOCUMENTATION ..................................................83

BIBLIOGRAPHY ..............................................................................................................92

xii

LIST OF TABLES

Table Page

Table 1. Sample weight to thickness ratio guideline for orthotics prescribers .................36

Table 2. Data used to build the surrogate models for each scenario ................................39

Table 3. Deflection for Instron experimental tests vs. ANSYS WB deflection

values. ....................................................................................................................42

Table 4. Comparison of clinical trials data vs. ANSYS WB uniform load

deflection values. ...................................................................................................44

Table 5. Comparison of clinical trials data vs. ANSYS WB varying distributed

load deflection values 30/70. Light = 0.040MPa (88lbs), Medium =

0.074MPa (160lbs), Heavy = 0.138MPa (300lbs) .................................................46

Table 6. Comparison of clinical trials data vs. ANSYS WB varying distributed

load deflection values 60/40. Light = 0.040MPa (88lbs), Medium =

0.074MPa (160lbs), Heavy = 0.138MPa (300lbs) .................................................47

Table 7. Light scenario surrogate model compared to finite element model values

and percent difference for the Response Surface, Kriging, Non Parametric

Regression, and Neural Networking methods. ......................................................58

Table 8. Medium scenario surrogate model compared to finite element model

values and percent difference for the Response Surface, Kriging, Non

Parametric Regression, and Neural networking methods. .....................................58

Table 9. Heavy scenario surrogate model compared to finite element model

values and percent difference for the Response Surface, Kriging, Non

Parametric Regression, and Neural networking methods. .....................................59

Table 10. Clinical, uniform load and distributed load deflection values compared

using standard error and P-values ..........................................................................64

Table 11. Results from uniform and 30/70 simulations compared to clinical

results. The deformations are in negative z direction. The number in

parenthesis under the clinical deflection are standard deviation. ..........................73

Table 12. Weight Distribution Regional Mean Values and SD (N=107)

(Cavanaugh, 1987). ................................................................................................75

Table 13. Pressure distribution (%) for various loading conditions with

corresponding deformation Mean (SD) of N=10 ...................................................76

xiii

Table 14. Optimal Design Variable Pressure Distributions and corresponding

deformation values from various Goal Driven Optimization Techniques .............78

Table 15. Uniform, 30/70 and Optimal Pressure FEA results compared to clinical

data (the deformations are in the negative z-direction) .........................................79

Table 16. Optimal Plantar pressure Distribution for medium subject..............................80

xiv

LIST OF FIGURES

Figure Page

Figure 1. Custom foot orthotics manufacturing process flowchart ....................................3

Figure 2. a) Imbalanced spine due to foot pronation (or a low arch), b) balanced

spine .........................................................................................................................4

Figure 3. Four layers of a semi-rigid style custom foot orthotic ........................................5

Figure 4. Boundary conditions applied to FEA model simulating the midstance

phase of gait: (a) Zero DOF in the vertical direction on the bottom area

(arch left unconstrained), (b) Zero DOF in the underside of the heel region

in all directions, (c) Zero DOF in the horizontal direction on the back,

lateral and front edge, (d) uniform surface pressure load applied to the

entire top surface. ...................................................................................................13

Figure 5. Maximum deflection vs. the applied load by orthotic thickness. .....................14

Figure 6. Stress distribution view (a) top and (b) bottom. ...............................................14

Figure 7. (a) ankle-foot orthtotic, (b) accomodative orthotic ..........................................18

Figure 8. Experimental set-up for orthotic in Instron machine in MIE materials

laboratory ...............................................................................................................28

Figure 9. Uniformly distributed surface load application ................................................29

Figure 10. Orthotic used for clinical trials including tracking markers ...........................30

Figure 11. Cantilever beam material set-up including 1”x 3” rectangular bar of

polypropylene. A strain gage was glued onto the polypropylene bar and a

5N load was applied at a distance of 56mm from the clamp .................................33

Figure 12. ANSYS WB model, (a) Medial side view showing arch alteration

lines, (b) top view showing Instron 15mm diameter load location and

alteration lines as well as 30mm diameter constraints. ..........................................34

Figure 13. Split load application (30% of load applied to back/heel portion of the

model) ....................................................................................................................45

Figure 14. Surrogate models for the light load scenario (A) Response Surface,

(B) Kriging, (C) Non Parametric Regression, (D) Neural networking. .................49

xv

Figure 15. Surrogate models for the medium load scenario (A) Response

Surface, (B) Kriging, (C) Non Parametric Regression, (D) Neural

networking. ............................................................................................................51

Figure 16. Surrogate models for the heavy load scenario (A) Response Surface,

(B) Kriging, (C) Non Parametric Regression, (D) Neural networking. .................53

Figure 17. Two-Variable Face-Centered CCD ................................................................55

Figure 18. Two-Variable Rotatable CCD ........................................................................56

Figure 19. Two-Variable Inscribed CCD .........................................................................57

Figure 20. Effect of load location holding thickness and load constant separated

by arch ht. Only 3mm used for example, all thicknesses are similar. (A)

is the 60N load, (B) is the 140N load and (C) is the 200N load. ...........................68

Figure 21. Varying arch height (only 3mm is shown, other orthotic thicknesses

are similar) .............................................................................................................69

Figure 22. The 10 anatomical regions that result from regional division

(Cavanagh, 1987). ..................................................................................................74

Figure 23. (a) ANSYS workbench CFO model showing midline division, (b)

ANSYS workbench CFO model displaying imprinted faces for

redistributed plantar pressure distribution. ............................................................76

1

CHAPTER 1

INTRODUCTION

Today’s competitive manufacturing environment has placed a great importance

on the ability to reduce the time, effort, and expense pertaining to the iterative decision-

making process used in design of products. Engineering design typically requires the

collaboration of resources from mathematics, science, engineering and technology to

optimally convert resources to meet the desired needs (BMED, 2001). The quality of

engineering design and the inherent cost of ensuring such quality are two critical

attributes which will always be conflicting with each other. In general, a higher quality

design outcome typically requires higher developmental costs. Therefore, it is critical for

engineering decision makers to find the best method of minimizing their developmental

cost while still maintaining the highest quality possible. In addition, information

technology in conjunction with global free trade policies, encourage a significantly large

increase in competition from all over the world (Haythornthwaite, 2006, Goldman, 1999).

This surge of competition logically brings about price wars in which profit margins may

decrease all the way to a negative point if the product developing costs are not

sufficiently low (Curedale, 2003). When developing a product, over 70% of life-cycle

costs are expended during the design phase (Shao, 2007, Anderson, 2003). The quality of

the design outcomes has the largest impact on the engineering decision maker.

Engineering designs are driven by customers’ needs, yet constrained by their

buying power and the small window of opportunity to enter the market before unknown

competitors flood the market (Michalewicz, 2004). Therefore, a constant demand is

placed on engineering decision makers to be more efficient and productive in producing

2

superior designs (Blunkett & Johnson, 2005). “This requires a results-driven, effective

and efficient engineering design framework that facilitates the finding of optimal design

solutions at the minimum cost.” (Shao, 2007, Sobieszczanski, 1997).

Proper knowledge and understanding of how body forces are applied and the

mechanics of the interaction between the body and orthotic can facilitate the development

of optimally designed orthotics. Significant advancements in the understanding of

kinematics and dynamics of human motion, as well as in the design and development of

medical devices to enhance human performance, can offer new paradigms for the holistic

solutions to the challenges faced when quality of life is compromised. On the basis of

these considerations, this research aims to demonstrate how engineering modeling,

analysis and optimization can significantly enhance the design and development of the

Custom Foot Orthotic (CFO), a widely used performance enhancement device.

With over 50 CFO manufacturers and over half of North Americans in need of

orthotic intervention (Christopher Maclean, former president of PFOLA and director of

Biomechanics at Paris Orthotics), there is still little scientific evidence in the literature to

support the positive results seen by patients throughout the years, due to the effects of

stress redistribution and accurate foot shape support. This research offers

recommendations of methods to use that will further our understanding of the effects that

CFOs have on human movement and performance.

3

The current CFO manufacturing process is described in Figure 1. It is evident

that there are many steps in this process, which makes it a timely and expensive process.

Incorporating engineering modeling will allow increased efficiency of the manufacturing

process.

Figure 1: Custom foot orthotics manufacturing process flowchart (Image credits in order of appearance to: No Aestetic [http://sal2009.com/index.php?key=Orthotics], Podiatrytoday.com, ProLab

Orthotics [http://www.prolaborthotics.com/Education/Casting/CastEvaluationFunctional/tabid/226/Default.aspx], direct industrial [http://www.directindustry.com/prod/cnc-step-hylewicz-cnc-technik/3d-laserscanner-64456-442366.html],

http://www.oguiadacidade.com.br/video/easycad/, Thermwood blog [http://blog.thermwood.com/?Tag=5%20Axis], No Aestetic.)

Many people who are in need of orthotic intervention either cannot afford

them or are not willing to pay the price for a treatment that does not have concrete

positive claims. (Trinidad, 2008) People from varying communities use orthotics,

from frail elders to athletes and everyone in between. Orthotics are typically accepted

as a method for resolving ailments by altering the position of the foot, which in turn

alters the lower extremities and one’s alignment all the way up the body. Figure 2

http://sal2009.com/index.php?key=Orthotics

http://www.prolaborthotics.com/Education/Casting/CastEvaluationFunctional/tabid/226/Default.aspx

http://www.directindustry.com/prod/cnc-step-hylewicz-cnc-technik/3d-laserscanner-64456-442366.html

http://www.oguiadacidade.com.br/video/easycad/

http://blog.thermwood.com/?Tag=5%20Axis

4

demonstrates how a spine can become imbalanced by the pronation of the left foot.

This pronation causes the leg to shorten which causes the hip to tilt which in turn

causes the opposite shoulder to dip.

Figure 2: a) Imbalanced spine due to foot pronation (or a low arch), b) balanced spine (image credit to: Gibsons Chiropractic Clinic and Marotta Health and Wellness chiropractic)

The formal definition of an orthotic is “a support, brace, or splint used to support,

align, correct or prevent the function of moveable parts of the body” (Medicinenet, 2007).

Shoe inserts are orthotics that are intended to “correct an abnormal, or irregular walking

pattern, by altering slightly the angles at which the foot strikes a walking or running

surface” (Medicinenet, 2007). Over the last ten years, there has been an incredible

increase in the use of CFO’s as evident by the increased volume of foot orthotics

manufactured and the number of new orthotic labs (Richie, 2006). With the increase in

production, CFO prescribers want more knowledge about orthotic therapy, but one

obstacle is the lack of uniform information (Richie, 2006). Another is the high cost of the

is corrected Foundation When

http://www.medterms.com/script/main/art.asp?articlekey=3499

5

intervention, without clear concrete evidence guaranteeing positive results; a typical pair

of CFOs ranges from three to five hundred dollars (Feldman, 2010).

Figure 3: Four layers of a semi-rigid style custom foot orthotic (Image credit to: Kintec FootLabs)

A semi-rigid style orthotic is a functional foot orthotic “used to partially control

abnormal motion or abnormal position of the foot and leg during gait”

(www.PFOLA.org/technicaltopics). The most popular materials used to make up a

typical semi-rigid style orthotic are polypropylene, EVA foam, Spenco™, Topy, and

McPuff (Figure 3). For the support material, polypropylene and graphite composite

comprise 98% of the CFO that are made (Richie, 2006). For the purposes of this research

we will not be discussing graphite composite.

Presently, clinicians calculate the stiffness of the orthotic based on their

experience using the patient’s characteristics (i.e. arch height, foot and body mechanics,

weight and activity level) and the orthotic design (selected material: orthotic shell, top

cover, posting material, alterations to the cast, and additions to the orthotic). In the

future, it seems possible to produce interactive software wherein the clinician can

complement traditional clinical methods with engineering models so as to produce

orthotics that are optimal for each particular client. Towards this end, this research

investigates the application of engineering modeling, analysis and modeling methods in

6

the design of CFOs. As part of this research, analysis models using finite element

analysis methods will be developed and their results will be verified and validated based

on experimental and clinical studies. Surrogate models will be developed through the use

of Response Surface Methods and Kriging techniques to further enhance the

computational efficiency of the design process. The following section details the specific

aims of this research and their significances.

Statement of the Problem

Previous research (Trinidad, 2008) detailed a simulation-based design procedure

for the systematic design of CFOs. Findings showed that when properly employed, the

models have the potential to enhance the prescription process by complimenting current

practices. Further extending this simulation-based approach to include predictive models

will enable optimal design of CFOs based on an individual person’s body weight,

activities, loading conditions, foot functions, etc.

Specific Aims

Study 1

Specific Aims #1:

The specific aims of study 1 are to develop refined Finite Element Analysis

(FEA) simulation models to mimic CFO behaviors under loading and validate the results

through clinical and experimental results. These tasks are important because the FEA

model of the custom foot orthotic is the first of its kind. CFOs have not yet been studied

using FEA to date. These models provide a starting point for further research on CFO’s

using FEA. Verifying and validating these models will ensure that the model mimics real

orthotic behavior.

7

The tasks include: a) running a clinical trial to validate the model, b) running an

experimental trial to verify the model, and c) investigating the influence of arch height

and load location on arch deformation. The challenges involved in these tasks include

designing experimental and clinical studies to asses and validate FEA model assumptions

and criteria, and altering the FEA model to account for various arch heights and load

locations. The FEA model geometry was created using a laser scanned image of the

physical orthotic and converting the image to a CAD model. Altering the geometry will

involve transferring the model to Solidworks (a CAD software) and creating a program to

modify the geometry. When designing the experimental and clinical trials, it is difficult

to apply all of the assumptions made in the development of the model. For instance, the

model does not contain a floor meaning there is no friction involved. Although in the

clinical and experimental setting the friction between the floor (or base of fixture) and

orthotic is very small and assumed to be negligible, there is still a difference. Another

difference is the shape of the orthotic. The orthotic in the model was built from a sample

orthotic, whereas the orthotics used in the clinical trial are tailor made for each subject.

The difference in geometry can affect model variables including length of the device,

heel depth, and arch height. In the experiment the orthotic must be held down by a clamp

in two spots to prevent the orthotic from sliding and twisting. In the lab the orthotic is

double stick taped to the bottom of the subject’s foot, which will prevent the foot from

fully expanding and deflecting the arch completely. Although there are some challenges,

these studies will greatly enhance the current CFO research. FEA is a tool that can allow

access to experiments not necessarily possible in a clinical trial, and its tools have not

fully been utilized in the investigation of CFOs to date.

8

Study 2

Specific Aims #2:

The specific aims of study 2 are to develop surrogate models and design

procedures to augment currently used empirical tables in the CFO prescription process.

The empirical tables are a reference used by clinicians assigning orthotic thicknesses to

certain weighted individuals (Table 2 in methods section). This study is important

because simulation models are computationally costly. One can incorporate many

different variables in a surrogate model without re-running a costly FEA model.

The challenges include obtaining enough data to support the development of

accurate surrogate models as well as validating the surrogate models. Research tasks

include building the RSM, Kriging, non-parametric regression and neural network model

from the FEA data using thickness, deflection and arch height as a function of weight. It

is hypothesized that the surrogate models will accurately mimic the FEA model

simulations and the resulting response surface will produce visual representation of the

input and output variables to replace empirical tables currently used.

Significance of the studies

Although orthotics have become widely used and accepted as devices for the

prevention of and recovery from injuries, the design process continues to be based on

empirical means. A deeper understanding of the therapeutic effects of a CFO and its

design for optimal performance can be achieved through systematic simulation-based

engineering modeling and analysis studies.

9

There has been very little conclusive research done pertaining to the

biomechanical influence of custom foot orthotic intervention. The majority of the

clinical studies performed to date have resulted in conflicting results due to significant

limitations such as experimental design or subject selection (Maclean et al., 2006).

Research applied to many rehabilitation devices is inconclusive due to many

uncontrollable factors, as is the case with research relating to CFO’s. Some of these

factors include “the large variability of individual foot types, differing philosophies on

foot function and a large variety of materials as well as types of orthotics” (Feldman,

2010).

This research stipulates that biomechanics research can be improved when clinical

studies are coupled with rigorous engineering methodologies. This research expands on

the understanding of human movement and performance through modeling, simulation

and analysis. Accordingly, it is the goal of this research to apply engineering modeling

and analysis to better understand the therapeutic effects of orthotics and to give insight

into the best method of research suited for future work and practical application in this

area. Therefore, these simulation-based modeling, analysis and corresponding results

offer a promising new approach to optimal design and development of CFOs.

Summary

Although orthotics are accepted as an effective means of treating and preventing

injuries, it may take months for results to be seen because the prescription process is

primarily one of qualitative means. Patients may also hold back on purchasing orthotics

due to the high cost. In addition, patient compliance may be lower than desired due to a

lack of scientific basis for the claim to positive results.

10

This research aims to verify and validate the finite element model previously

created, replace empirical tables with design charts using surrogate models, and offer

greater freedom in experimental design as well as in the CFO prescription process.

By adding these results to the CFO community the design process may become more

efficient, and the product may therefore become more affordable and accessible to all

population and groups.

Previous work

FEA model of a Custom Foot Orthotic

Introduction

In previous research we presented an engineering approach to the modeling and

analysis of Custom Foot Orthotics (CFOs). The development of a methodical simulation-

based approach using Finite Element Analysis (FEA) is outlined. Salient steps for the

development of accurate CFO models include the creation of FEA models through

approximation of complicated material properties, as well as a methodical process for the

replication of the complex three-dimensional geometry.

Despite the common practice of modeling and analysis through FEA in product

design, tools related to these systems have not been utilized when designing custom

prescription foot orthotics. This is primarily due to the fact that the engineering analysis

is complex and the dynamics of human gait characteristics are difficult to model. This

work further extends the use of FEA to model and analyze prescription CFOs.

11

Methods

1) Nonlinear Material Property Estimation

An initial challenge when creating a FEA of CFOs results from the limited

availability of material properties. This challenge is compounded by the highly complex

and nonlinear traits of these materials. For this study, we considered the most popular

material used in typical semi-rigid style CFOs: polypropylene. Ten sample sheets of

polypropylene with varying thicknesses (2mm, 3mm, and 4mm) provided by Kintec

Footlabs were examined using ASTM standard D575-91, and D412. Material properties

were approximated through uniaxial tensile testing and resulting stress-strain behaviors

were constructed.

To capture the nonlinear material properties, the Mooney-Rivlin strain energy

function was adopted and the constants were calculated (Finney, 1988) and can be

expressed as:

S = 2(a-a-2

) (C1+C2*a-1

); G = 2*(C1+C2) (1)

where S is stress, a is the principal stretch ratio (1+dL/L), and material constants C1 and

C2 relate to the shear modulus, G = 2240MPa. The constants C1and C2 are derived from

plotting the equation:

(S/(2*(a-a-2

))) vs. a-1

(2)

These equations will form a line, where C2 is equal to the slope of the line, and C1 is

equal to the intercept at a-1

= 1. C1 = -22623 and C2 = 23743.

12

2) Geometry Construction

The replication of CFO geometry using CAD tools is extremely time consuming

and almost impossible to accurately represent. An alternative approach involves using

laser scanning technology to generate the geometry. Laser scanning captures an object’s

geometry in a point cloud surface image, simplifying the process while creating the most

accurate result. In this project, a semi-rigid CFO was scanned using a laser digitizer and

the point cloud image was converted into a solid image using 3-Matic, a commercial

imaging tool from Materialise Inc.

3) Modeling of Constraints and Loads

Engineering analyses rely on the identification of kinematic constraints and

applied forces. The mid-stance phase of gait was modeled, as this is a good starting point.

The following boundary conditions were applied: 1) zero degrees of freedom (DOF) in

the underside of the heel region; 2) zero horizontal movement on the back, lateral and

front edges; and 3) zero movement in the vertical direction on the bottom area. The arch

area was left unconstrained. Finally, a uniform surface pressure load was applied, to

simulate mid-stance, using a static large deflection model to the entire top surface. These

boundary conditions can be seen below in figure 4.

13

Figure 4: Boundary conditions applied to FEA model simulating the midstance phase of

gait: (a) Zero DOF in the vertical direction on the bottom area (arch left unconstrained),

(b) Zero DOF in the underside of the heel region in all directions, (c) Zero DOF in the

horizontal direction on the back, lateral and front edge, (d) uniform surface pressure load

applied to the entire top surface.

4) Results

The ANSYS finite element package was used to run the analyses on three

separate weight classifications (Trinidad, 2008) and the maximum von Mises stress and

deflection results were acquired (Figures 5 and 6).

Figure 5 is a plot of the applied load versus the deflection of the arch area using

three weight classifications. Each line represents a different model which only varies by

thickness. The larger the load applied, the more deflection is seen in the arch. The

thicker the model the less deflection there is.

14

Figure 5: Maximum deflection vs. the applied load by orthotic thickness.

Figure 6 shows a representative plot of the von Mises stress distribution which

shows that the maximum stress areas are around the edge of the arch.

Figure 6: Stress distribution view (a) top and (b) bottom.

5) Discussion & Summary

This research details the successful development of a simulation-based design

procedure for the systematic design of custom foot orthotics. Properly employed, these

models may enable optimal CFO designs based on a patient’s body weight, activities,

loading conditions, foot deformities, etc. Finally, these models and the corresponding

results promise to form the basis of a new generation of custom foot orthotics. The

obvious next step is to figure out if the model is estimating the CFO behavior accurately.

This leads us to the current studies verifying and validating the FEA model to correspond

to CFO behavior.

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.2 0.4 0.6 0.8 1 1.2

Applied Load (MPa)

De

lec

tio

n (

mm

)

2mm

3mm

4mm

5mm

15

CHAPTER 2

LITERATURE REVIEW

Introduction

The following section provides a review of the literature concerning orthotics

research using FEA and background on surrogate modeling. This section begins with a

comprehensive review of orthotics research through clinical studies and followed by a

more in-depth examination into the use of Finite Element modeling. It ends with an

introduction to surrogate modeling and how it can be used as a tool to complement the

current CFO prescription process.

Orthotics

As mentioned above, Custom Foot Orthoses (CFOs) are often used as an

acceptable method of managing injuries, and while they usually produce encouraging

outcomes, it still remains unclear how the dynamics of the lower extremity are influenced

by the device (MacLean et al., 2006). Many previous clinical studies have been

performed on the effects of CFO intervention, and many have focused specifically on the

effects during running. These studies have focused on rear foot and tibial kinematics, and

both lower extremity kinematics and kinetics (MacLean et al., 2006). Variability has

been seen in study results due to two main reasons: 1) the types of subjects used; and 2)

the design of the experiment (MacLean et al., 2006).

Many research investigations have distributed identical designs to each subject in

order to limit the confusing effects of the orthotic (Mundermann et al., 2003). It has been

argued that using the same orthotic design for all subjects could be just as or more of a

puzzling factor, given that the resulting device may not be comfortable or suitable for

16

each subject’s needs (MacLean et al., 2006). CFOs are usually prescribed by podiatrists,

physical therapists and sports medicine physicians (Root, 1994) and then manufactured

from a volumetric impression of the foot by a certified laboratory to address the specific

needs of the patient. CFO research has not always included subjects who would normally

be candidates for the intervention; many studies have utilized healthy or injury-free

subjects (MacLean et al., 2006).

The main findings from CFO clinical studies have been: significant decrease in

maximum rearfoot eversion angle (Bates et al., 1979; Smith et al., 1986; MacLean et al.,

2006), decrease in maximum rearfoot eversion velocity (Smith et al., 1986; MacLean et

al., 2006), decrease in maximum internal ankle inversion moment (Mundermann et al.,

2003; Williams et al., 2003; MacLean et al., 2006), decrease in impact peak and

maximum vertical loading rate (Mundermann et al., 2003), and decrease in maximum

tibial internal rotation angle (Nawoczenski et al., 1995).

Although these studies have shown results, these results have been considered

somewhat ambiguous due to the questionable experiment designs mentioned above.

Therefore, the actual effects orthotics have on the kinematics of human locomotion

remain unclear due to the fact that it is either extremely difficult, very time consuming or

not possible to design a study that will incorporate the appropriate subjects and

investigations. This has limited researcher’s ability to draw strong conclusions regarding

the design and effect of CFOs. This is where modeling and analysis can assist in the

progression and facilitation of this research. Modeling allows for the ability to control

subject variability, thereby minimizing some of the uncertainty found in the current

literature.

17

Orthotics & Finite Element

It has been publicized by many researchers that biomechanical factors play a

crucial role in the study of orthotics. (MacLean, 2006) Little biomechanical data is

available in the literature to assist in understanding how such factors can effectively be

applied to the development of orthoses. It is possible to simulate foot motions, change in

material properties, different loading conditions, and different orthotic conditions using

accurate FE models. These models can be altered relatively easily, making it possible to

further our understanding on the influence that the device has on biomechanical factors.

Currently, the majority of FEAs on orthotics have focused on two types of

orthotic inserts: Ankle-Foot Orthotics, or AFOs, and accommodative orthotics (Figure 7).

AFO research has focused on analyzing stress points found in the device when in use.

This research has allowed for optimal designs leading to the reduction of orthotic fracture

and increase in patient compliance. On the other hand, research on accommodative

orthotics has primarily focused on the reduction of peak plantar pressure in the hopes of

preventing foot ulcerations. Both will be addressed further in the following sections.

18

Figure 7: (a) ankle-foot orthtotic, (b) accomodative orthotic

Ankle Foot Orthotic Finite Element Analysis Research

AFOs are designed to help control the motion of the ankle while offering support

to the foot. They are often used to treat conditions such as drop-foot, posterior tibial

tendon dysfunction, severe flatfoot, arthritis of the ankle and/or foot, ankle sprains, lateral

ankle instability and tendonitis.

There are three major objectives for the design of an AFO. The first is to control

motion, correct deformity, and compensate for weakness, thereby restoring normal

function and ability. The second objective is to make the orthotic as comfortable to wear

as possible in order to increase patient compliance. The third objective is to minimize the

abnormal appearance of the orthotic. Most advanced AFOs have been unable to improve

on all three objectives. The goal of most early research was to either reduce the weight or

bulkiness of the orthotic to increase patient compliance or strengthen the weak spots that

tend to fail due to high stresses applied by the foot.

Early studies using FEA on AFOs investigated the response of the ankle with and

without orthotics (P.C. Lam et al., 1986) by analyzing peak stresses and deformation

patterns. Later studies used FEA to predict loads at which AFOs become unstable and

analyze the stress distributions (D. Leone et al., 1991; T-M Chu et al., 1991). More

19

recent work on AFOs includes a study using FEA to suggest improvements on lowering

the weight and improving the comfort of an orthotic by evaluating real time pressure

between the subject and the orthotic during routine actions (walking, chair rise, stair

climb, pivoting) via a resistive pad. From the collected data, an accurate model of the

orthotic was created and the stress caused by the above activities was evaluated, leading

to modification suggestions to reduce orthotic weight (Khamis S. Abu-Hasaballah et al,

1997). Most recently, FEM was used to determine optimal design features (strut

thickness) prior to implementing into the AFO manufacturing process (Faustini, 2008).

Accommodative Orthotic Finite Element Analysis Research

Accommodative orthotics are primarily used for the prevention of foot ulcers

through the reduction of plantar pressure levels by redistributing the stresses between the

foot and orthotic. Foot ulcers are a serious problem for people suffering from diabetes as

it can lead to foot amputation and ultimately death. Neuropathy and vascular disease are

complications associated with diabetes, and although both may be present, the pathology

results in either sensory deficit (neuropathy) or vascular impairment (vascular disease).

Skin ulcerations are a result of chronic sensory neuropathy. A protective threshold is

when a person possesses adequate sensation to determine when his or her body is at risk

of harm from an outside source. At any point below this threshold, there is inadequate

sensation to signal the brain to potential harm. When the protective threshold is lost, this

allows repetitive, painless trauma to occur to soft tissues and skeletal structures which

may further increase the sensory deficit.

Friction, pressure and shearing are the three causes of stress and of great concern

for diabetics. Friction is the surface resistance of one body sliding over another. Blisters

20

are caused by fast and constant friction; the opposite causes calluses. The vertical ground

reaction forces applied to the foot is referred to as pressure. Ischemia can be caused by

constant pressure and can result in necrosis (tissue death). Shearing is a combination of

friction and pressure and can occur when two surfaces slide over each other, with

pressure being applied perpendicular to the direction of movement. This force is often

produced during normal gait. These forces can cause potential injury to the bones and

soft tissues (joint subluxation and skin ulceration).

Orthotic therapy is intended to decrease Ground Reaction Forces (GRF) applied

to the foot. An exact mold of the foot is extracted and if localized areas of pressure

occur, the GRF can be reduced by elevating adjacent areas, such as with metatarsal pads.

Distributing GRF over a greater time period will decrease shearing. For example, soft

materials will slow the foot by increasing the vertical distance the foot travels before

coming to rest. If the orthotic materials are rigid the poor shock absorption and non-

accommodative properties will not be helpful for these patients. Corrective components

of orthoses aim at decreasing unnecessary pressure on the foot by limiting excess motion

and maintaining an unstable foot in proper alignment.

Reduced plantar pressure levels to prevent foot ulcers can be achieved with in-

shoe orthoses. They reduce the pressure at bony prominences, especially under the

metatarsal heads. Although this method is readily used, very little actual quantitative

information is available regarding the effect of thickness and influence of soft tissue

characteristics on the cushioning effect of these orthoses. FEA has been used to analyze

accommodative orthotics mostly in the late 1990s and most recently in 2006. Nonlinear

material properties are difficult to model and only with recent computing advancements

21

has this become more common. The first study used FEA to compare insoles of varying

thicknesses by calculating peak plantar pressures and validating these models and values

through clinical measurements (Lemmon et al., 1995). Two years later this same group

investigated alterations in pressure under the second metatarsal head as a function of

insole thickness and foot tissue thickness. The group found that orthoses reduced plantar

pressure and offered techniques which allowed for a better approach to understanding

plantar cushioning as well as the principals involved in the design of therapeutic footwear

(Lemmon et al., 1997). More recently in Chen et al.’s 2003 research, FEA was used to

study the effects of total contact insoles on plantar stress redistribution by analyzing

different stress reduction and redistribution. This research allowed for recommendations

to be made on the effectiveness of accommodative orthotics.

In 2005, Erdemir’s group took a comprehensive look at plantar pressure relief in

footwear with compliant material plugs. 36 plug designs were looked at: 3 materials, 6

geometries, and two placements. In Barahi, 2005, they looked at reducing the plantar

pressure levels specifically under the hallux. 3-D models of the insoles were constructed

and analyses were run comparing 4 different materials: silicone gel, plastozot, plyfoam,

and EVA. And finally in Actis 2006, they developed a patient-specific mathematical

model of the second and third rays of the foot. Different models of the foot were

constructed with varying levels of detail with the foot in the push off position. They used

quasi-linear material properties for the TCI by taking the slope of first and last linear

portion and a 2nd

order spline to connect the two linear portions. There have been some

recent studies on the foot insole interaction, but these studies have primarily been

emphasizing the finite element model of the foot as opposed to the orthotic.

22

Currently nothing comparable exists in the literature regarding the application of

FEA to the understanding and design of CFOs and, more specifically, semi-rigid style

custom foot orthotics.

State of the Art

In the most recent and sophisticated research, a detailed FEA model of a foot was

created and the stress distribution under the foot for several types of orthotics were

studied (Cheung, 2008) Cheung’s research focused on different combinations of

structural and material design factors on plantar pressure distribution. The sensitivity of

six design factors, arch type, insole and midsole thickness, insole and midsole stiffness,

and custom molded shape, of foot orthosis on peak plantar pressure relief. Custom

molded shape was found to be the most important factor in reducing peak plantar

pressure. The insole stiffness was found to be the second most important feature for peak

pressure reduction. Statistics based FE method was found to be an effective approach in

evaluating and optimizing the design of foot orthosis. The research developed in this

research focus on enhancing the custom molded shape and looking at varying the arch

height to analyze the effects on stiffness.

Metamodeling

Modeling is a tool used to complement the design process and make it more

efficient. Models are abstractions from reality (Hazelrigg et al., 1999). They simulate

the behavior of a physical system in specific circumstances using performance variables

in order to project the behavior of that system. These models offer a cost efficient way to

view system performance and offer practical solutions without the use of physical

models. Many engineering analysis models can be computationally costly; some may

23

take hours or days to run a single simulation (Shao, 2006). Metamodels (or Surrogate

models) are models of models that are one level of abstraction away from an original

design or analysis model and can be used to make computations more efficient.

Although they are simplifications of models, they still maintain critical characteristics of

the original models (Shao, 2007, Simpson, 2004).

Although computer-model-based design methods have been increasingly popular

and almost necessary in the engineering design process, the creation of complex and

accurate numerical models can still require exorbitant computational costs. Complex

models such as a coronary stent expansion simulation by Shao 2007 was reported to take

91 hours to complete on a Pentium 4 computer with 3Ghz CPU and 780MB available

physical memory, and 512KB cache memory, (Shao & Krishnamurty, 2006,

Krishnamurty & Shao, 2005) even if only 1/24th

portion of bare metal stent was included

in the model. Shao speculates that “if the pressuring balloon, coronary arterial tissues,

and the irregularity in human tissues were considered in the stent model, the computer

simulations would have taken weeks or even months to get the results” (Shao, 2007).

Numerical models with such complex high definition details make design optimization

incredibly difficult and in some cases impossible. In order to arrive at an optimal design

anywhere between a dozen to hundreds of simulation runs are usually required. These

challenges are therefore compounded if each simulation requires several updates at each

feasible point before successful convergence (Booker, 1999). Alternatively, surrogate

models built as statistical approximations to these computationally expensive numerical

models have been increasingly popular in accelerating the process in design and

optimization.

24

The fundamental idea in surrogate-model-based design is to develop a less costly,

more efficient mathematical approximation to the costly numerical model based on

simulation data collected from a small number of runs of the more expensive numerical

model. This surrogate model is then used alternative to the original simulation model to

assist in “design space exploration, design optimization, reliability analysis, etc…” (Shao,

2007) (Krishnamurty & Wilmes, 2004, Simpson, 2004). Surrogate model simulations

frequently take less than one second. Designers can gather extensive information about

unknown systems using surrogate models without paying large computational costs.

Once a high-fidelity numerical model is created, information about the system to

be designed is collected through a small number of sample points corresponding to

various design alternatives. A surrogate or metamodel (typically used interchangeably), a

statistical approximation of the numerical model is then created from the sample data.

Successive designs and optimizations are executed using the surrogate model. The

subsequent design modifications are more efficient than in the numerical-model-based

design approach. Therefore efficiency of design optimization and reliability analysis can

be greatly improved with a good surrogate model. Designers can use surrogate models to

get extensive insight into unknown system without paying a heavy computational price.

Summary

Traditionally, custom designing orthotics has been a process primarily using

empirical methods. Very little actual quantitative information is available regarding the

effectiveness of CFO’s and little scientific evidence is available to provide guidelines for

persons who prescribe insoles. Engineering modeling and analysis techniques allow for

the possibility of significant contributions to CFO research community as well as a

25

greater understanding of interactions between foot and orthotic. Due to the challenge

involved in the multi-layering of the soft and hard materials of the CFOs, only the

polypropylene support phase will be looked at in this research.

26

CHAPTER 3

METHODOLOGY

General Introduction

The goal of this dissertation is to introduce alternative methods of researching

CFOs; by evaluating how engineering modeling, analysis and optimization can enhance

the design and advancement of CFO’s. Very little definitive quantitative information is

available regarding the effectiveness of custom orthotics and little scientific evidence is

available to provide guidelines for persons who prescribe insoles. This research

investigated methods that will allow for an increase in scientific evidence to CFO

influence as well as provide practical applications of these methods to practitioners.

This goal was accomplished in the two separate studies outlined below.

Study 1

Introduction

This study involves the verification of FE models of CFOs with experimental

trials, the validation through clinical trials, and the investigation on the influence of

arch height and load location on the deformation of the arch.

The model has been verified through Instron® testing, and the completion of

the validation took place in the Biomechanics Lab in the Kinesiology Department.

A clinical trial with three subjects allowed us to validate the simulated behavior of

the model to accurately represent the behavior of CFOs. The final analysis was to

investigate the effect of varying desired variables in the FEA by varying arch height

and load location in the model. By varying these factors we can investigate how

27

these factors affect the performance of the orthotic, as well as show the flexibility of

the model.

Verification and Validation

The purpose of this study was to develop refined FEA simulation models to

mimic CFO behaviors under loading and validate the results through experimental data.

These tasks are important because the FEA model of the custom foot orthotic is the first

of its kind. CFOs have not yet been studied using the Finite Element Method (FEM) to

date. These models provide a starting point for further research on CFOs using FEA.

Verifying and validating these models will ensure that the model mimics real orthotic

behavior.

A Finite Element model was created using the ANSYS package where a custom

foot orthotic is modeled with specific geometry and material properties, as described in

the previous work (Chapter 1). We will be discussing the task of running an

experimental trial to verify the model.

Experimental set-up and stress analysis

We wanted to perform an experiment in a controlled setting where we could test

and verify the material property behavior of the FEA model. Therefore, the

experimental trial was performed on an Instron machine in the materials lab of the

Mechanical and Industrial Engineering department at the University of Massachusetts

Amherst. Multiple orthotics of varying thicknesses were clamped onto a metal plate on

the heel and front edge of the orthotic. Then the plate was placed securely into the

Instron machine (Figure 8).

28

Figure 8: Experimental set-up for orthotic in Instron machine in MIE materials

laboratory

Since the primary area of interest is the deflection of the arch area, the load was

concentrated so that it would deflect the arch while minimizing the effects of the

compression of the material. Therefore, a 15mm diameter point load was applied onto

the highest point of the arch (measured to be 7.5mm from the front edge) of the orthotic.

Three different loads were applied (60N, 140N and 200N). These values were chosen to

describe a range of loads, but loads heavier than 200N resulted in the buckling of the

orthotic. The model was then run in ANSYS WB to simulate the Instron experimental

tests with a concentrated 15mm area load.

Clinical trial and data collection

This model was also tested by running clinical trials and comparing them to the

model values. The model was run in ANSYS WB with a uniform load applied to the

29

top surface in order to simulate the mid-stance phase of walking and compared to the

clinical trial data (Figure 9).

Figure 9: Uniformly distributed surface load application

In order to test and validate the simulation results, a clinical study was

performed with three subjects of varying weight (Light: 0.040MPa (88lbs), medium:

0.073MPa (160lbs) and heavy 0.138MPa (330lbs)). The study involved two sessions.

During the first session, the subjects came into the lab to measure their weights and cast

their feet. The cast of their feet was sent to Kintec Inc. for the manufacturing of the

orthotics. Once the orthotics were ready, the second session involved the data

collection. Specifically, six reflective markers were placed on the rim of the orthotic

placed at the following positions: 1) 75% of the total length (medial), 2) 50% of the

total length (medial), 3) 50% of the total length (lateral), 4) center of the heel cup

(medial), 5) Center of the heel cup (lateral), 6) on the back rim at 50% of the total width

(Figure 10). The markers were placed in these areas in order to decipher the 3

dimensional motion analysis raw data. Markers 1, 2 and 4 gave the curvature of the

30

arch which allows the measurement of the change in height of the arch by looking at

marker #2 as compared to markers 1 and 4 in the z-direction. Marker number 6 gives

the midpoint of the orthotic and the motion of the heel or rear foot as well as the change

in marker #2 compared with marker #6 in the x-direction. The lateral markers (3 and

5), give a frame of reference when looking at the data from the front or back and shows

the change in arch height in the y-direction.

Figure 10: Orthotic used for clinical trials including tracking markers

With the markers placed on the orthotic, the orthotic was adhered to the

subject’s foot using double stick tape. The subjects were asked to complete three tasks:

1) stand on one leg, 2) walk and 3) run. Each of these tasks was completed with the

orthotic attached to one foot and only that foot touching the force platform.

Prior to collecting data, the orthotic was placed on the force platform in the

center of the cameras to collect a non-weight-bearing data set. The cameras recorded

the position of the reflective markers. This was done to get a baseline reading of the

31

marker positions and arch height of the orthotic. This task was repeated 2-3 times. For

the first task, the subject was asked to stand on the force platform on the one foot that

has the orthotic attached to it. The subject used a stick to assist with balance, and the

subject held this position for approximately 10 seconds. That task was repeated

approximately 5 times. For the second and third task the subject was asked to walk then

run from one end of the laboratory to the other across the force platform making sure to

place the foot with the orthotic attached to it on the force platform. This took

approximately 10 seconds and was repeated 10 times for each activity. A three

dimensional movement analysis system quantified movement patterns of the reflective

markers during each trial. Subsequently, the clinical study results were compared to the

simulation results to further refine and validate the simulation models.

Subjects

An informed consent (Appendix) was required for the subject. The individual

must be 10 - 60 years of age, healthy as per a Modified Physical Activity Readiness

Questionnaire (Appendix) and not have had any surgeries in the lower extremity or foot

area. This study consisted of the subject completing one task for the data collection

phase. This session took approximately 30 minutes.

Experimental set-up

A custom semi-rigid style orthotic was manufactured for the subject. The

orthotic was measured on its own for baseline measurements of the arch height. The

subject stood on the device and the weight was translated down to deform the foot

and in turn the arch. The amount of deflection the arch experiences was recorded.

There were tracking markers on the arch and were recorded using the camera system

32

in the biomechanics lab at the University of Massachusetts Amherst. The deflection

was compared to the values seen in the FE model.

Data reduction

Marker traces for each trial will be processed and identified in Qualysis TM

software, and computations will be performed in Visual 3DTM

and MatlabTM

software.

Based on the movements of the markers, three dimensional movement patterns for the

arch of the CFO were computed. Starting with a baseline measurement of the CFO

position without any weight applied, and the subjects’ weight was applied to the CFO.

The position of the triangulation of markers outlining the curvature of the arch are

captured in both the non-weight bearing position and the applied weight position and

compared. The change in height of the highest marker was used as the resulting value

for deflection of the arch.

Cantilever beam test

Many researchers have compared the human foot and in particular the arch area

to a beam (Cavanagh, 1987& Steindler, 1955). Originally the material properties for

this finite element model were calculated using uniaxial tensile tests (mode 1) to get the

modulus of elasticity through tension. Upon further thought and realizing that the

majority of the deformation seen on the arch of the orthotic was through bending and

shear similar to what a beam would experience, the decision was made to test the

material properties through a cantilever beam test (Mode 2).

The cantilever beam test was performed using a 1”x 3” rectangular bar of

polypropylene which was clamped into an Instron machine (Figure 9). A strain gage

was glued onto the polypropylene bar and a 5N load was applied at a distance of 56mm

33

from the clamp. The strain was collected and the stress calculated using the bending

stress equation (Juvinall, 2006):

(2)

where M is the bending moment, h is the thickness of the sample (in meters), and I

is the moment of inertia. This equation can be derived for our purposes to a more

useful format:

(3)

where P is the load applied (5N), Δl is the length of the active portion of the beam

(l3 – l2 = 0.046m), b is the width of the beam (0.02m), and h is the thickness of the

beam (0.003m). These calculations yielded a stress of σ =7.67MPa. The average

strain measured by the Instron was ε = 0.003134 after 5 trials with a Standard

deviation of .000012. Young’s modulus was calculated from the stress and strain

collected to be 2446MPa. For the uniaxial tensile testing E was calculated to be

4480MPa for the 3mm heated polypropylene which is about double the modulus of

elasticity calculated using the cantilever beam test.

Figure 11: Cantilever beam material set-up including 1”x 3” rectangular bar of

polypropylene. A strain gage was glued onto the polypropylene bar and a 5N load was

applied at a distance of 56mm from the clamp

34

Varying load location and arch height

In order to alter the arch height and concentrated load location the model was

transferred into Solidworks. A Solidworks VBA macro developed by Krishna

Samavedam was used to generate and parameterize the control points for splines. The

arch height ranged from 16mm (from the floor/base fixture) to 25mm (from the

floor/base fixture) as seen in Figure 12 (a). The concentrated load location ranged from

55mm (from front edge) to 80mm (from front edge) as seen in Figure 12 (b).

(a)

(b)

Figure 12: ANSYS WB model, (a) Medial side view showing arch alteration lines, (b)

top view showing Instron 15mm diameter load location and alteration lines as well as

30mm diameter constraints.

35

The following operations are performed when this macro runs.

1. The control points that are sampled on the STL model of CFO are imported into

Solidworks.

2. Three lines are drawn along X, Y and Z axes to control the coordinate location

of the control point.

3. Dimensions are assigned for each line.

4. Parametric equations are generated between the dimensions and the parameters.

This Solidworks model was attached to the ANSYS WB model and the modifications

were made automatically depending on the desired design point to be analyzed.

Summary

This study evaluated the use of FEAs ability to investigate design changes and

their effects on the device by investigating the influence of the arch height in reducing

stresses. This study also validates the FE model previously described in the

introduction by evaluating the effectiveness of these models to mimic CFO behavior.

The change in arch height (deflection) during the clinical trials is compared to the

change in arch height (deflection) in the model.

Study 2

Introduction

The purpose of metamodels is to provide approximation models for structuring a

design problem, increase the speed of computing, and make the design process more

efficient. They simulate the behavior of the actual system as close as possible in a more

economical way by using simpler approximations through least squares regression or

interpolation methods. In this study metamodels of the FE model were developed and

36

a tool for clinicians’ to replace empirical tables (Table 2) to use in the office to

compliment current prescription processes was suggested.

Experimental set-up

The objective of a routine statistics-based performance model is to mimic the

systems input/output behavior based on the collected data distributed over the design

space. ANSYS has the ability to run surrogate models using four different methods:

Full second order polynomial standard Response Surface Method (RSM), Kriging, Non

Parametric Regression (NPR), and Neural Networking (NN). This study compares the

accuracy and efficiency of each of the four methods.

Response surface uses a least square regression fitting method, whereas Kriging

uses the same method to fit the overall trend of the data, while also calculating the

errors associated with the correlation of the distance between data points. The non

parametric regression “is a form of regression analysis in which the predictor does not

take a predetermined form but is constructed according to information derived from the

Table 1: Sample weight to thickness ratio guideline for orthotics prescribers

37

data.” (McCune, 2006) The Neural Networking method is inspired by the structure

and/or functional aspects of the human brain. It has the ability to learn and can change

its structure based on pattern adapted from the learning phase. Neural Networks are

used to model relationships between inputs and outputs or to find patterns in data. The

Neural Networks learning capabilities work by using a set of observations to define a

relationship between the input and output data in some optimal sense (Smith, 1993).

ANSYS Workbench explores a relationship between the design variables X1

(arch ht) and X2 (orthotic thickness) and the response variable Y (deflection) to form an

approximation model (a response surface) of the data. Three design surfaces were

created for each loading scenario; each scenario was used to create a design surface for

the three different load classifications designated as: light (0.040MPa), Medium

(0.074MPa) and Heavy (0.138MPa). The design surface was created using 15 design

points, the design points were chosen at the three arch heights: 16 (low), 20.5 (medium)

25 (high), for each orthotic thickness: 1.5mm, 2mm, 3mm, 4mm and 5mm. These

surrogate models can be used to explore other uses and effects of custom foot orthotics

without running the full finite element model. Additional variables may also be added

to explore other situations without changing the finite element model. Although these

surrogate models are proven to be more efficient by saving time, the loss of accuracy

during the “approximation” was investigated with respect to the usability of the results.

Validation

Once the surrogate models were built, each model was validated and the results

compared to its deviation from the original finite element model. The validation of the

models was executed by building another data set using a rotatable central composite

38

design (Montgomery, 1997). This new data set contains only input values and the

output values were from the surrogate model. These output values were compared to

the original finite element model output values and compared by % difference. It is

important to know how much accuracy the surrogate model is maintaining while

approximating the full model. The rotating central composite design will allow the

retrieval of data from each quadrant of the approximation surfaces directly at points

used to create the model as well as at points not used to create the model.

Model Building:

The models were built in ANSYS WB using four different methods; Response

surface, Kriging, non parametric regression and neural networking. The different

methods use different approaches to creating a relationship between the input and

output data used to build the model. Three different arch heights and five different

orthotic thicknesses were used to build the models. The data used are shown in the

table below:

39

Table 2: Data used to build the surrogate models for each scenario

Light (0.040MPa)

Medium (0.074MPa)

Heavy (0.138MPa)

Arch Ht Thickness deflection



16 1.5 6.79

16 1.5 12.35

16 1.5 23.15

16 1.5 6.79

16 1.5 12.35

16 1.5 23.15

16 2 3.92

16 2 7.13

16 2 13.36

16 3 1.85

16 3 3.37

16 3 6.31

16 4 1.12

16 4 2.04

16 4 3.83

16 5 0.79

16 5 1.44

16 5 2.71

20.5 1.5 8.57

20.5 1.5 15.59

20.5 1.5 29.24

20.5 2 4.49

20.5 2 8.17

20.5 2 15.32

20.5 3 1.97

20.5 3 3.59

20.5 3 6.73

20.5 4 1.20

20.5 4 2.18

20.5 4 4.09

20.5 5 0.86

20.5 5 1.57

20.5 5 2.94

25 1.5 10.46

25 1.5 19.03

25 1.5 35.69

25 2 5.39

25 2 9.81

25 2 18.40

25 3 2.26

25 3 4.11

25 3 7.71

25 4 1.34

25 4 2.45

25 4 4.58

25 5 0.96

25 5 1.75

25 5 3.28

Summary

There is much that is still unknown in the general area of CFOs. Modeling is a

tool that can greatly improve the methods in which are used to determine the

effectiveness of orthotics. These surrogate models will not only provide tools to make

the CFO research and prescription process more scientific and optimal, but it may also

provide a possible tool for clinicians to use in the office to replace the empirical tables

they currently use. This study determines the cost-to-benefit ratio of the four methods

used to build each surrogate model by comparing the efficiency and accuracy of each

method. While these methods have never been used in the study of CFO, these studies

will allow for the application of much more efficient design and development of CFOs.

40

Summary

It is important to understand which methods are the best methods to proceed

with in future research. Although clinical trials are currently the most common

technique used for CFO investigation, previous work in Trinidad (Trinidad, 2008)

showed that FEA models may be less time consuming and allow for more variability in

the design of experiments and provide concrete results to the current data collected

through clinical trials. The incorporation of surrogate models may allow for even more

freedom and efficiency and allow for better practical application.

41

CHAPTER 4

RESULTS

Study I

Instron Verification

The Instron tests were run using different size orthotics with various thicknesses,

applying a 15 mm round point load to the highest point of the arch (approximately 50%

of the length on the medial side of the orthotic). This point load was also applied to the

FEA model and the difference in means, standard deviation, and sample size were

compared using a paired-t test. The resulting P-value was used to measure the precision

in the sample mean, since we are estimating the overall population average for our

comparisons. The P-value is defined as the probability that one data set is as much as or

more extreme than the other observed data set if the null hypothesis was true (Evans,

2011). The null hypothesis states that the FEA model data and the clinical trial data

are equivalent:

H0: Dfea=Dclin,

Ha: Dfea≠ Dclin

An alpha level of 0.05 was used as is conventional in clinical studies. “Statisticians

have found that approximately 95% of all randomly selected sample means fall within 2

units of standard error from the population mean” (Batavia, 2001, Ch. 11).

There were three different size orthotics used for these studies; a small

(women’s size 5), a medium (women’s size 7.5) and a large (men’s size 16). Each size

orthotic was made in 3 different size thicknesses (between 2mm, 3mm, 4mm and 5mm).

Corresponding models were created in ANSYS and the arch deflection was compared.

42

The means, standard deviation and percent error are compared between the

experimental (Instron) tests and the ANSYS model trials. The loads applied were 60,

140 and 200 N applied as a 15mm concentrated load on the highest point of the arch.

The results between the ANSYS model (Trinidad, 2008 & Chapter 1) and the

Instron tests show very good agreement and verify that the ANSYS models can

reproduce real world behavior as can be seen in Table 4 below. The percent differences

between the two sets of results are mostly less than 5%, and the probability values

indicated that there is no significant difference between the two methods. There are

three values that are above 5% difference, (Medium orthotic, low load, and large

orthotic, low and medium load) but they are still below 15% difference and the p-values

still indicate no significant difference in the values.

Table 3: Deflection for Instron experimental tests vs. ANSYS WB deflection values.

Small

Load (N)

Instron Deflection δ (mm)

Standard deviation

Standard error

Model Deflection δ (mm)

% Difference P-Value

60 1.532 0.04 0.02 1.56 1.81 0.26

140 3.222 0.11 0.05 3.24 0.56 0.77

200 4.376 0.21 0.09 4.24 3.16 0.29

Medium

Load (N)


Standard deviation

Standard error


% Difference P-value

60 2.392 0.80 0.36 2.13 11.59 0.56

140 5.078 0.28 0.13 4.97 2.15 0.50

200 6.97 0.41 0.18 7.1 1.85 0.57

Large

Load (N)


Standard deviation

Standard error


% Difference P-value

60 2.64 0.88 0.40 2.34 12.24 0.54

140 5.544 1.41 0.63 6.44 14.95 0.29

200 7.814 0.53 0.24 7.45 4.83 0.26

43

Clinical Validation

Uniform Surface load

The clinical validation was run using three subjects light, medium, and heavy;

each subject had different orthotics of varying thicknesses to test. The light subject had

a 2mm, 3mm, and a 4mm thick orthotic. The medium subject had a 2mm, 3mm, and a

4mm thick orthotic to use. The Heavy subject had a 3mm, 4mm and a 5mm thick

orthotic to use. Although we collected data for all 9 scenarios, we chose to focus on the

3mm and 4mm data in order to compare all three subjects to each other for each

condition. Their body weights were converted into a pressure load (Pa) and those

values were inserted into corresponding models that were created in ANSYS as a

uniform surface load and the arch deflection was compared to the clinical trials. We

began with a simplified uniform surface load, although a person’s weight is not

uniformly distributed throughout the bottom of their foot, it was a reasonable starting

point (Figure 7). Statistical data were calculated (% difference, mean, standard

deviation, and P-value) between the model and clinical data.

Although, the clinical trials show less agreement with the ANSYS model as

compared to the experimental Instron trials, the agreement is satisfactory as the majority

of the P-values are greater than 0.05 demonstrating that there is no significant difference

between the two data sets except for the heavy 3mm condition.

44

Table 4: Comparison of clinical trials data vs. ANSYS WB uniform load deflection

values.

3mm (2.78mm)

Load (Pa)

Clinical deflection CL_SD

Model deflection

% Difference in Means P-value

δ (mm) δ (mm) α = 0.05

Light 2.22 0.52 2.10 5.56 0.68

Medium 3.00 0.25 3.84 24.56 0.13

Heavy 5.56 0.06 7.25 26.37 0.02

4mm (3.78mm)

Load (Pa)


Model deflection

% Difference in Means P-Value

δ (mm) δ (mm) α = .05

Light 1.06 0.18 1.20 12.39 0.47

Medium 1.82 0.39 2.20 18.67 0.15

Heavy 3.95 0.34 4.20 6.13 0.33

Varying distribution load

After running the model with a uniform surface load it was observed that the

agreement was satisfactory but could be improved if the loading characteristics in the

model were adjusted. The uniform surface loading was a simplified loading

distribution, but an appropriate place to start from. While investigating the loading

characteristics and weight distribution of a normal person during the stance phase of

walking (Cavanagh, 1987 and Cheung, 2005), it was noted that the weight is not

uniformly distributed but distributed at different levels throughout the foot, generally

separated by heel, forefoot and midfoot, in that order. A much smaller percentage of

the weight is seen in the arch of a foot (midfoot area). Since some of the research has

reported that normal stance is generally observed as approximately 25% – 45%

(Morton, 1953) of the weight in the heel, and some has reported that 60% of the weight

is loaded in the heel, we decided to redistribute the weight looking at both theories

45

(Figure 13). The first redistribution was accomplished by applying 30% of the weight

in the heel section of the model and the second by applying 60% of the load in the heel.

The orthotic is only a three-quarter orthotic leaving a portion of the forefoot

unrepresented. The weight was redistributed first by dividing 30% of the weight in the

back of the orthotic and the other 70% of the weight in the rest of the model, and second

by dividing 60% in the back of the orthotic and 40% of the weight in the rest of the

model.

Figure 13: Split load application (30% of load applied to back/heel portion of the

model)

Making this adjustment showed much improvement in the agreement with the

clinical trials showing more consistency and reducing the error between them. These

distributed load models seem to be a slightly more accurate representation of normal

human loading behavior and the accuracy between the clinical trials and the model

increased for most of the scenarios. The accuracy increased by decreasing the percent

difference while still maintaining a p-value greater than 0.05 for most of the scenarios.

Tables 6 and 7 show the comparison of the clinical trial data to the ANSYS 30/70 load

46

distribution and 60/40 load distribution respectively. A further, more comprehensive

investigation of the loading distribution is required to further improve upon the loading

characteristics in the model, but this is an appropriate next step.

Table 5: Comparison of clinical trials data vs. ANSYS WB varying distributed load

deflection values 30/70. Light = 0.040MPa (88lbs), Medium = 0.074MPa (160lbs),

Heavy = 0.138MPa (300lbs)

3mm (2.78mm)

Load (Pa)


Model deflection


δ (mm) δ (mm) α = .05

Light 2.22 0.52 1.59 33.24 0.09

Medium 3.00 0.25 2.89 3.81 0.65

Heavy 5.56 0.06 5.41 2.68 0.18 4mm (3.78mm)

Load (Pa)


Model deflection


δ (mm) δ (mm) α = .05

Light 1.06 0.18 0.94 11.83 0.52

Medium 1.82 0.39 1.71 6.29 0.61

Heavy 3.95 0.34 3.21 20.62 0.06

47

Table 6: Comparison of clinical trials data vs. ANSYS WB varying distributed load

deflection values 60/40. Light = 0.040MPa (88lbs), Medium = 0.074MPa (160lbs),

Heavy = 0.138MPa (300lbs) 3mm (2.78mm)

Load

(Pa) Clinical

deflection CL_SD Model

deflection % Difference

in Means P-value

δ (mm) δ (mm) α = .05

Light 2.22 0.52 1.59 33.07 0.09

Medium 3.00 0.25 2.90 3.39 0.67

Heavy 5.56 0.06 5.55 0.20 0.85 4mm (3.78mm)

Load

(Pa) Clinical

deflection CL_SD Model

deflection % Difference

in Means P-value

δ (mm) δ (mm) α = .05

Light 1.06 0.18 0.75 34.25 0.25

Medium 1.82 0.39 1.37 28.44 0.10

Heavy 3.95 0.34 2.61 40.85 0.02

Study II

The four surrogate models are built for each finite element model. The following

graphs (Figures 14, 15 and 16) show the resulting surrogate models from each of these

methods over the design space for the light, medium, and heavy weight scenarios. In

the figures 14, 15 and 16 (A) is the result of the response surface method, (B) for the

Kriging Method, (C) is the non parametric regression method and (D) the neural

network method. Each surrogate model took about one second to run.

48

(B)

AA

(A)

AA

49

Figure 14: Surrogate models for the light load scenario (A) Response Surface, (B)

Kriging, (C) Non Parametric Regression, (D) Neural networking.

(D)

AA

(C)

AA

50

(B)

AA

(A)

AA

51

Figure 15: Surrogate models for the medium load scenario (A) Response Surface, (B)


(D)

AA

(C)

AA

52

(B)

AA

(A)

AA

53

Figure 16: Surrogate models for the heavy load scenario (A) Response Surface, (B)


(C)

AA

(D)

AA

54

Model Validation:

Once the surrogate model surfaces were built, a rotatable central composite

design was used to validate these models. Experimenters typically use experiment

designs that consist of trial runs at the lower and upper extreme points (Montgomery,

1997). The Design of Experiments method was chosen based on the desired regions to

be analyzed in the most efficient way. The central composite design (CCD) is the most

commonly used design of experiments methods for three main reasons. (1) CCDs can

be run sequentially. It can be partitioned into two subsets of points; the first estimates

linear and two-factor interactions, and the second estimates curvature. (2) They are

very efficient, providing a lot of information variable relationships and experimental

error in a minimum number of required runs. And (3) CCDs are very flexible. The

variability in available CCDs enables their use under different experimental regions of

interest and operability (Verseput, 2000).

There are three main types of CCDs used: face-centered (FCCCD), rotatable

(RCCD) and inscribed (ICCD). The FCCCD encompasses the extreme points as well as

the midpoints of the region. The design consists of a center point, four factorial points

and four axial (extreme) points. The dots in Figure 17 define the variables that

constitute the nine design points (experiment runs).

55

Figure 17: Two-Variable Face-Centered CCD

“The radius, designated α, determines the geometry of the design region. An α of 1.0

defines a square design geometry (a cube for three variables, a hypercube for four or

more variables, etc.).” (Verseput, 2000).

If the precision of the estimated response surface at some point x depends only

on the distance from x to the origin, not on the direction, then the design is said to be

rotatable (Oehlert 2000). The variance remains the same when the rotatable design is

rotated about the center. The rotatable CCD is shown in Figure 18.

56

Figure 18: Two-Variable Rotatable CCD

The inscribed option is a convenient way to generate a rotatable CCD that

allows the experimenter to study the entire range of the variables while excluding

unacceptable conditions at one or more of the extremes of the design region (Verseput,

2000). The downside to this method is that it restricts the actual design region. This

design is generated by locating the axial points at the lower and upper bounds of the

variables, the factorial points are then set at a specific distance from the center point

maintaining the proportional distance between the factorial and axial points and

inscribes these points into the interior of the design space (verseput, 2000) This can be

seen in Figure 19 below where the excluded portion of the region is shown in gray, as

are the excluded face-centered CCD points.

57

Figure 19: Two-Variable Inscribed CCD

The reason for using a rotatable design in this research is that it provides equal

precision of estimation of the surface in all directions. The rotatable CCD produced 9

points (as seen in Figure 18) and the output at the four surrogate models were compared

to the output for the original model at each point. Five of the nine points were used to

create each surrogate model and the other four are intermediate points spaced at

different zones of the surface. Table 7 shows the summary of results for the light

weight scenario. This table compares the differences in deflection values from the

original FEA results when using the different surrogate models. Tables 8 and 9 show

the summary of results for the corresponding medium and heavy weight scenarios.

58

Table 7: Light scenario surrogate model compared to finite element model values and

percent difference for the Response Surface, Kriging, Non Parametric Regression, and

Neural Networking methods.

(mm) (mm (mm) (mm) (mm) (mm) (mm) deflection vs. RSM

deflection vs. Kriging

deflection vs. NPR

deflection vs. NN

Arch Ht

Thickness

FEA model RSM Kriging NPR

Neural Network

% difference

% difference

% difference

% difference

16.00 3.00 1.85 1.79 1.85 1.85 1.86 3.30 0.00 0.00 0.66

18.25 2.00 4.14 4.21 4.17 3.96 4.17 1.53 0.64 4.52 0.63

20.50 1.50 8.57 8.49 8.57 8.57 8.56 0.87 0.00 0.00 0.04

22.75 2.00 4.94 4.93 4.90 4.96 4.95 0.22 0.83 0.44 0.20

25.00 3.00 2.26 2.25 2.26 2.26 2.07 0.44 0.00 0.00 8.92

22.75 4.00 1.26 1.29 1.26 1.09 1.24 2.12 0.13 14.63 1.60

20.50 5.00 0.86 0.87 0.86 0.86 0.87 0.72 0.01 0.00 0.61

18.25 4.00 1.17 1.19 1.16 0.94 1.17 1.44 0.60 21.95 0.09

20.50 3.00 1.97 2.02 1.97 1.97 1.95 2.38 0.01 0.00 0.97

Average 1.45 0.25 4.61 1.52

Table 8: Medium scenario surrogate model compared to finite element model values

and percent difference for the Response Surface, Kriging, Non Parametric Regression,

and Neural networking methods.

(mm) (mm) (mm) (mm) (mm) (mm) (mm) deflection vs. RSM


deflection vs. NPR

Deflection vs. NN

Arch Ht

Thickness

FEA model RSM Kriging NPR

Neural Network

% difference

% difference

% difference

% difference

16.00 3.00 3.37 3.29 3.37 3.37 3.39 2.19 0.00 0.00 0.65

18.25 2.00 7.54 6.20 7.59 7.20 7.59 19.42 0.67 4.52 0.65

20.50 1.50 15.59 15.43 15.59 15.59 15.59 1.04 0.00 0.00 0.04

22.75 2.00 8.98 9.29 8.91 9.02 9.01 3.36 0.82 0.45 0.25

25.00 3.00 4.11 4.12 4.11 4.11 3.76 0.07 0.00 0.00 8.97

22.75 4.00 2.30 2.40 2.29 1.98 2.26 4.34 0.05 14.75 1.50

20.50 5.00 1.57 1.54 1.57 1.57 1.58 1.74 0.00 0.00 0.76

18.75 4.00 2.12 1.86 2.11 1.83 2.14 13.33 0.54 14.89 0.68

20.50 3.00 3.59 3.62 3.59 3.59 3.55 0.75 0.03 0.00 1.01

Average 5.14 0.23 3.85 1.61

59

Table 9: Heavy scenario surrogate model compared to finite element model values and

percent difference for the Response Surface, Kriging, Non Parametric Regression, and

Neural networking methods.

(mm) (mm) (mm) (mm) (mm) (mm) (mm) deflection vs. RSM


Deflection vs. NPR

Deflection vs. NN

Arch Ht

Thickness

FEA Model RSM Kriging NPR

Neural Network

% difference

% difference

% difference

% difference

16.00 3.00 6.31 6.16 6.31 6.31 6.35 2.49 0.00 60.86 0.63

18.25 2.00 14.13 11.51 14.23 13.51 14.22 20.41 0.67 64.93 0.65

20.50 1.50 29.24 28.80 29.24 29.24 29.22 1.49 0.00 0.00 0.04

22.75 2.00 16.84 17.46 16.70 16.92 16.89 3.62 0.82 0.45 0.25

25.00 3.00 7.71 7.74 7.71 7.71 7.06 0.36 0.00 0.01 8.89

22.75 4.00 4.30 4.49 4.30 3.71 4.24 4.23 0.01 14.69 1.45

20.50 5.00 2.94 2.90 2.94 2.94 2.96 1.29 0.00 0.01 0.73

18.25 4.00 3.98 3.32 3.93 3.20 3.98 18.13 1.24 21.81 0.00

20.50 3.00 6.73 6.79 6.73 6.73 6.66 0.84 0.00 0.00 0.98

Average 5.87 0.30 18.09 1.51

For the light weight data set, it appears that Kriging offers the best model with

least error over the actual FEA model, followed by the response surface model, then

neural networking and finally the non parametric design. For the Medium data, the

Kriging offers the best results, followed by the neural network method, the non

parametric regression and finally the response surface model. For the Heavy data,

Kriging again has the best results, followed by the neural network, then the response

surface, and the non parametric regression model. From the results, Kriging is the only

method that is consistently accurate for all weight classes, with less than 0.3%

difference. Each of these models within each weight category also took less than one

second to run, which is an almost 200% saving of time.

60

CHAPTER 5

DISCUSSION & CONCLUSIONS

Study I

Two studies were performed, one to verify and one to validate the finite element

model; the first study involved comparing the FEA model to an Instron test. This

deterministic test is a direct proportion of load and stresses. There was no minimal

variance between the analysis and the experimental trials. The second study involved

the comparison of clinical trials to the FEA model using a uniform load applied to the

entire surface. Although the clinical trial data were limited, the results compared

reasonably well. Most of the values were within 20% difference of each other and the

majority of the P-values were indicative that there were no significant differences

between the two data sets (there were a few outliers). This loading distribution was a

starting point since in reality people do not stand with their weight evenly distributed

across the entire foot. The majority of the weight is distributed between the heel and

ball of the foot and then a smaller portion of the weight falls in the middle of the foot

(arch area) (Cavanagh, 1987, Hills, 2001, Birtane, 2004, Morton, 1953). To make the

loading conditions more accurate, the models were refined by altering the load applied

to the surface of the orthotic, making it more realistic to the actual load distribution seen

under a foot during the stance phase of walking. We split up the load by 30% of the

total weight in the heel of the foot as some research has suggested that the heel and

forefoot are more equally loaded (Morton, 1953). Since the orthotic is a three-quarter

orthotic and the model is only split into two, back end (heel) and front end (midfoot and

part of the forefoot) we split the load into two parts, 30% in the backend, and 70% in

61

the front end. This proved to yield more accurate results which reduced the difference

between model and clinical data significantly for four of the six scenarios. Specifically,

in the 3mm thick orthotic, the differences were lowered for the medium and heavy

subjects, but increased for the light subject. For the 4mm thick orthotic the percent

difference was lowered for the medium and light subjects, but increased for the heavy

subject. For this redistribution, the P-values indicated that there was no significant

difference between the model and clinical values. Although this load distribution

minimized the errors between the model and clinical data for the majority of the

scenarios, this improvement was not consistent.

A second re-distribution of the weight was applied to the model based on

Cavanagh’s findings, which reported that they found that 60% of the weight is held in

the heel. We re-distributed the load using 60% of the weight in the heel, and 40% in the

front of the orthotic. This new distribution of load proved to also decrease the percent

difference for the medium and heavy subject for the 3mm thick orthotic, but less

accurate with the 4mm orthotics, where the percent differences actually increased for all

three subjects. Although the P-value indicated that there were still no significant

difference between the model and clinical values for the light and medium loads,

concluding that this distribution of weight can still be used to model the behavior of

human loading conditions on orthotics for light and medium subjects. The heavy

scenario P-value indicated that there is a significant difference between the model and

clinical values for the 4mm orthotic.

These validated FEA models allow for the further investigation of orthotic

intervention. These models enable easy alteration of geometry and loading conditions

62

for use in practical applications. The challenges involved in these tasks included

designing experimental studies to match FEA model assumptions and criteria. When

designing the experimental and clinical trials it was difficult to apply all of the

assumptions made into the development of the model. For instance, the model does not

contain a floor suggesting there is no friction involved. Although in the experimental

setting the friction between the floor (or base of fixture) and orthotic is very small and

assumed to be negligible, there is still a difference. Another variation is the shape of the

orthotic. The orthotic in the model was built from a sample orthotic, whereas the

orthotics used in the clinical trial were specifically made for each subject. The

difference in geometry can affect the performance such as: length of the device, heel

depth, and arch height to name a few variables. The length of the device is also a

factor, as it is only 75% of the foot’s total length and since we are applying 100% of the

subject’s weight to the orthotic, the elimination of the weight held in the 25% of the

foot that is not supported by the orthotic is not taken into account. Although this is a

very small percent of the total weight, it could account for some of the discrepancies.

Finally, in the clinical trials, the subjects were holding on to a broomstick to assist with

balance. This broomstick was used to stabilize the subject in order to minimize the

shifting of weight within the foot. Although the subjects were instructed to put as little

weight as possible on the broom stick, this will still take on some of the weight and

therefore make the weight applied to the orthotic less than in the model. While there

were some challenges and differences, the final values in the model correlated very well

with the experimental and clinical tests.

63

In the experimental tests the values matched the model to less than 15%

difference with 6 out of the 9 trials below 5% difference. For the clinical trials these

values are slightly less accurate in their match up as human subjects introduce many

other factors that affect these comparisons. These values are within 5 to 26%

difference, with most values below 15% difference. The data also indicate that there is

no significant difference according to the p-values above 0.05 except for the 3 mm

heavy category which has a p-value of 0.02. The large discrepancy in the 3 mm heavy

category is due to their only being one data set for the clinical trial, which caused the

standard deviation to be very small (0.05) so any difference in values is going to seem

like a large difference when discussing in terms of standard error and p-values. In this

uniform loaded model many of the difference in values may also be attributed to how

the person stands as opposed to how the weight was loaded into the model. If they

stand pronated, supinated or put more weight in their heel it would change the value in

which the arch is deflected.

We ran a second and third set by redistributing the weight in the model which

yielded more accurate loading conditions. The comparison of values to the clinical

trials also improved with both adjustments in weight distribution. Most of these data

lowered the comparison with the clinical trial to within 20% difference with most below

12%. Most of the P-values were also indicating that the data are not significantly

different except for the “Heavy” category. In addition to the differences in loading

characteristics of obese individuals to non-obese subjects, this smaller P-value in the

heavier load category may be due to the smaller variation in the heavier loads clinical

data causing each difference to have a greater effect.

64

One of the findings was that most of the load distributions were not very

accurate with the “Heavy” category. Although none of the load distributions were

consistently accurate, the uniform load distribution seems to be the most accurate for

the heavy subjects. Table 10 below includes the complete data set including the 5mm

data to compare all three cases for the heavy subject. Another possible difference

found for heavy subjects could be that these material properties may not be suitable for

heavy subject. The material properties were assigned based on an assumption that the

materials stay within the elastic range. The heavy subjects may possibly be heavy

enough to change the properties of the materials and therefore these material properties

may not be suitable for this population, especially for the thinner orthotics (3mm and

4mm thick).

Table 10: Clinical, uniform load and distributed load deflection values compared using

standard error and P-values

Clinical

Uniform load

FEA

Distributed

load(30/70)

Distributed load

(60/40)

δ (mm)

standard deviation

standard error ±2S.E.

δ

(mm)

P-

value

δ

(mm)

P-

value

δ

(mm)

P-

value

3mm

Light 2.22 0.52 0.23 2.68 - 1.76 2.1 0.68 1.59 0.09 1.59 0.09

Medium 3 0.25 0.2 3.39 - 2.61 3.84 0.13 2.89 0.65 2.9 0.67

Heavy 5.56 0.06 0.06 5.69 - 5.43 7.25 0.02 5.41 0.18 5.55 0.85

4mm

Light 1.06 0.18 0.11 1.27 - 0.85 1.2 0.47 0.94 0.52 0.75 0.25

Medium 1.82 0.39 0.18 2.18 - 1.47 2.2 0.15 1.71 0.61 1.37 0.1

Heavy 3.95 0.34 0.17 4.29 - 3.61 4.2 0.33 3.21 0.06 2.61 0.02

5mm

Heavy 2.89 0.1 0.05 2.99 - 2.79 3.13 0.05 2.3 0.01 1.5 0

These findings seem to be consistent with the research which states that obese

individuals demonstrate significantly different plantar pressures during both standing

65

and walking (Hills, 2001) flat footedness is also prevalent in obese subjects (Hills,

2001). The research has also found that the force distribution may shift forward into the

forefoot as bodyweight increases due to adipose tissue (Birtane, 2004). Therefore, it is

believed that a uniformly distributed load is more accurate for obese subjects. “Subjects

with higher arch index (representative of a flatter foot) demonstrate greater medial arch

lowering during the midstance phase of gait, and the movement pattern manifests as

increased loading under the midfoot.” (Menz, 2006)

Conclusion

The model verification and validation has been completed successfully. The

Instron tests deflection values were less than 15% different with six of the nine values

within 5% difference with the FEA model deflection values. The P-values greater than

alpha = 0.05 also indicate that there is no significant difference between the two data

sets. Most of the clinical trial values are below 26% difference, with 4 of the 7 values

below 15% of the FEA model deflection values and improving to below 22% when the

loading characteristics were altered to be applied more realistically. The P-values

between these two data sets also indicate that there is no significant difference between

the two data sets, except for in the heavy category. The differences that arise between

the experimental, clinical trials and the model are most likely caused by assumptions

made in the boundary conditions and other factors that cannot be prevented such as the

geometry, loading conditions, material thickness, as well as the lack of friction in the

FEA model.

This research shows that engineering analysis models using FEA can be used to

mimic the results found in clinical and experimental studies. The material behavior can

66

be modeled accurately using FEA techniques. We have identified an alternate means to

estimate the critical parameters that are crucial to custom design of orthotics based on

individual’s needs and characteristics. These validation studies prove that these models

can therefore be used to gain further knowledge and insight into the effectiveness of

orthotics. These studies will greatly enhance the current CFO research. FEA is a tool

that has not been fully taken advantage of in the investigation of CFOs and will be a

vital tool to further the body of knowledge on custom foot orthotics.

Case study: varying arch height and load location

This study started with a concentrated load along the arch area. The load

was moved along the arch (from anterior to posterior from 55mm to 80mm off the front

edge) to see what effect load location had on the arch deflection. This varying load

location model showed that as the weight is concentrated more towards the front of the

arch more deflection is seen, as well as if the load is concentrated towards the back, less

deflection is seen in the arch for most of the neutral and high arch designs. For the low

arches and the neutral arch in the medium weight category at its least towards the front

of the arch. It can be seen in Figure 20 below, where (A) is the result of the 60N load,

(B) is the 140N load and (C) is the 200N load:

67

1

1.1

1.2

1.3

1.4

1.5

1.6

40 50 60 70 80 90

De

fle

ctio

n (

mm

)

Force Application Location

Varying Load Location (60N Load)

60N @ Arch Height 16

60N @ Arch height 20.5

60N @ Arch height 25

2

2.2

2.4

2.6

2.8

3

3.2

3.4

3.6

3.8

40 50 60 70 80 90

De

fle

ctio

n (

mm

)




140N @ Arch Height 20.5

140N @ arch height 25

(A)

(B)

68

Figure 20: Effect of load location holding thickness and load constant separated by

arch ht. Only 3mm used for example, all thicknesses are similar. (A) is the 60N load,

(B) is the 140N load and (C) is the 200N load.

This is important for clinicians to know because if someone front loads their

weight they may need a thicker orthotic, whereas if someone who back loads their

weight may be able to get away with a thinner orthotic.

Next, the orthotic was fully loaded with a uniformly distributed pressure load

matching the weight of the subjects. We then looked at the effect of the arch height on

the arch deflection. As shown in Figure 21 below:

3

3.5

4

4.5

5

5.5

40 50 60 70 80 90

De

fle

ctio

n (

mm

)



200N @ Arch height 16

200N @ Arch Height 20.5


(C)

69

Figure 21: Varying arch height (only 3mm is shown, other orthotic thicknesses are

similar)

As the arch height changes so does the proportion of the arch deflection. The

higher the arch the less it deflects, so a person with a higher arch may be able to get

away with a thinner orthotic then for someone of the same weight with lower arches

depending on what their needs are.

Study II

Surrogate models are tools that can be quickly run in lieu of the full finite

element model in a more efficient manner. These models also allow for the ability to

minimize the error between a general template of an orthotic and specific patient’s

requirements of an orthotic. Specification of individual patient’s biomechanics, footfall

patterns, and activity level can be analyzed and added to the models quickly. Clinicians

can input specific factors into the surrogate models without having to run the full FEA

model, saving on ample computational time.

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

0 5 10 15 20 25 30

De

fle

ctio

n (

mm

)

Arch Height (mm)

Varying Arch Height (3mm Orthotic)

300lbs_3mm

140lbs_3mm

88lbs_3mm

70

We tested the performance of four algorithms on three design spaces. For each

model we looked at the percent difference between the Finite element model and the

surrogate model to assess the confidence of our results. The Kriging response surface

method seems to be the best out of the four methods. The average percent difference

for the Kriging method ranges between 0.23 and 0.30 %. The other methods range from

1.45 to 18% average difference. The time it takes to run the surrogate models were also

over 200% faster than the 6 minutes it took to run the basic FEA model. The small

values (below 0.5% difference) show that the Kriging method is accurate enough to be

used in lieu of running the full FE model and since the surrogate models run much

faster than the FE models, the Kriging method is more efficient without much loss of

accuracy. This method seems to be the best suited for predicting orthotic data and can

be used in the prescription process. These FEA models are in their most basic form,

once complexity is added to the models, so does the cost to run them. Adding patient

specification and non linear complex materials to create the full orthotic can multiply

the time to run by hours. It also may take several hundred FEA runs at each alteration;

the time savings for a specific CFO in office investigation for individual patients can be

much more feasible with the use of surrogate models.

Many of the other methods may work better with larger data sets, so it may be

possible to increase the accuracy of these other surrogate models by increasing the

model building data set. This may give the tools a better idea of the relationship

between the input and output information. The Kriging seems to work well with any

size data set due to the correlation function that performs a correction after each

71

iteration. The difference between the sample data and the Kriging function is calculated

and the function is adjusted according to the departure value.

When comparing the Kriging predictor model to Table 1, the values of the table

were slightly more conservative. As the table suggests that for a subject weighing

between 88lbs and 160lbs a recommended thickness for the orthotic is 4mm. The

clinical trial results demonstrated that for an 88 lb subject a 4mm orthotic will only

deflect approximately 1mm and for the 160lb subject the 4mm orthotic only deflected

1.82mm. This may be too stiff for both cases and cause the subject to have a thicker

orthotic unnecessarily. The Kriging predictor values are based on the clinical trial data

thereby demonstrating a more accurate guideline for clinicians to follow.

The Surrogate models are using the arch height and thickness of the orthotic to

create a relationship between the deflections of the arch, as can be seen from the

response surfaces in figures 14, 15 and 16. Although the arch affects the deflection as

was demonstrated by the first case study, the thickness is a much more determining

factor in the stiffness of the orthotic this is consistent with engineering principles.

Referring back to equation (2) the moment of inertia is the property of a beam that

predicts the resistance of beams to bending around the cross sectional plane. The

moment of inertia states that the stiffness is correlated to the thickness cubed.

Therefore the thickness is the main determinant in regards to stiffness of the orthotic.

Another draw to using surrogate models is the minimization of error through the

use of optimization. One example of the variability of use of these surrogate models for

optimal orthotic design is discussed in the case study below.

72

Case study: Force load distribution using surrogate modeling

In the previous study the validated finite element model of a custom foot

orthotic was introduced. This model simulated the stance phase loading simulation on

the surface of a custom foot orthotic using ANSYS WB. A simplified loading condition

was initially run, assuming the plantar pressure distributed uniformly across the entire

orthotic. Another set of simulations yielded a redistribution of the plantar pressure to

60/40, with 60% of the pressure in the heel and 40% in the front portion of the orthotic.

This set of simulations decreased the error between the uniformly distributed loaded

model and the clinical data. In another set of simulations the plantar pressure was

redistributed once more to 30% of the pressure in the heel and 70% in the front portion

of the model. For this study we will only be using the uniformly distributed load and

the 70/30 distribution for comparison.

The results plotted in Table 11 show a statistically significant amount of error

between the clinical data collected and the values obtained using FEA when using a

uniform loading condition. The resulting percent error and p-value for the 30/70

condition drastically improve. The percent error decreases by 15 to 24%, and the p-

value provides us with evidence that is not strong enough to reject the null hypothesis

that the Clinical and FEA data are equivalent. Overall, as the pressure distribution

across the orthotic better mimics the average plantar pressure of the human foot, the

smaller the percent error between the FEA model and clinical data and the greater the p-

value. Also note that up until this point percent difference has been used for the

comparison of values as neither value was regarded as the correct value the intent was

to evaluate the differences between them. For this study percent error is used because

73

the clinical data is considered the accepted value and we are comparing our results to

that value.

Table 11: Results from uniform and 30/70 simulations compared to clinical results.

The deformations are in negative z direction. The number in parenthesis under the

clinical deflection are standard deviation.

Loading Orthotic thickness

Clinical deflection accepted

FEA Model deflection measured

Percent Error

P-Value

t(mm) δ(mm) δ(mm) * **

Uniform 3 3.00 (0.25) 3.84 28 0.132

30/70 3 3.00 (0.25) 2.89 3.67 0.646

* [(Accepted-Measured)/Accepted]x100

** H0: δclinical = δFEA vs. HA: δclinical ≠ δFEA

The intent of this case study was to find the optimal plantar pressure distribution

for the finite element model to minimize the error between FEA model outputs and the

clinical data. This study was only run on the 3mm model of the medium weight subject.

Based on Cavanaugh’s 1987 plantar pressure distribution, the finite element model was

divided up into 10 anatomical regions depicted below in Figure 22. The weight

distribution regional mean values were used to portray a more accurate human plantar

pressure distribution. Cavanagh (Cavanagh, 1987) defined the 10 anatomical foot

regions using regional division method of footprints. Since the orthotic was cut off half

way between the metatarsal regions; the hallux, second toe and lateral toe will not be

considered. This eliminated region was only 3.6% of the total weight distribution so the

remaining regions equal 96.4%. The distribution of the weight along the pressure

regions according to Cavanagh (Cavanagh, 1987) is shown in Table 12.

74

Figure 22: The 10 anatomical regions that result from regional division (Cavanagh,

1987).

75

Table 12: Weight Distribution Regional Mean Values and SD (N=107) (Cavanaugh,

1987).

In order to attain an objective function for optimization, the CFO FE model was

altered in SolidWorks. The Geometry tool in ANSYS Workbench was then used to

imprint the 7 anatomical regions being investigated. In addition, ANSYS WB Design

Modeler and Mechanical were used to run various loading simulations to determine

which anatomical regions were most significant in arch deformation for the medium

subject. Finally, the Response Surface was created using the Kriging method in ANSYS

WB.

The original model was constructed with a division between the heel and forefoot

as shown in Figure 23(a). In order to create the 7 anatomical regions the division was

smoothed into a uniform surface and the anatomical divisions were imprinted onto the

top face and extruded down through all. The updated CFO FE model with anatomical

regions is shown in Figure 23(b).

76

Figure 23: (a) ANSYS workbench CFO model showing midline division, (b) ANSYS

workbench CFO model displaying imprinted faces for redistributed plantar pressure

distribution.

The load at each anatomical region was defined as a parameter that could be

altered in ANSYS to efficiently mimic the loading conditions outlined in Table 14. The

highlighted cells in Table 8 reflect the anatomical region that is maximized during the

particular loading condition. For example, someone who has a “medial heavy”plantar

pressure distribution focuses most of their weight on the medial side of their foot and

may possibly have flat arches.

Table 13: Pressure distribution (%) for various loading conditions with corresponding

deformation Mean (SD) of N=10

Region Average

Heel

heavy

Forefoot

heavy

Midfoot

heavy

Medial

heavy

Lateral

heavy

Medial heel 32.5 41.1 23.9 23.9 41.1 15.3

Lateral heel 28 36.2 50.6 20.6 20.6 36.2

Medial

Midfoot 1.4 2 1.2 2.5 2.5 0

Lateral

Midfoot 6.4 9 7.7 11.3 2.4 11.3

First MET 5.6 1.1 10.1 10.1 10.1 0.7

Second MET 8.4 4.6 12.2 7.3 12.2 12.2

LateralMETS 14.1 7.5 20.7 20.7 7.5 20.7

MEAN (SD) 2.96(0.074) 1.5(0.015) 4.47 (0.112) 4.33 (0.101) 5.36 (0.118) 1.09 (0.036)

(a)

(b

)

77

For each loading condition, the deformation of the highest point of the arch was

analyzed. At this location 10 sample data points were collected to determine the mean

deformations and the standard deviations presented in Table 13. From these results the

average plantar pressure distribution presented the most accurate deformation reading

when compared to the clinical data (3mm deflection). Therefore, for the remainder of

this study, an average plantar pressure distribution (Cavanaugh, 1987) was assumed for

the medium subject.

For the generated surrogate models, the data used were split up into two different

data layouts, the first (will be referred to as MH) using the Lateral heel (LH) and Lateral

metatarsals (LM) as input design variables, the calculated design variables being the

Medial heel (MH), and all other anatomical regions were constant. The second data

layout (will be referred to LM) was setting the MH and LH regions as input design

variables, LM’s region was the calculated design variable, and all other regions were held

constant.

A face centered central composite design was used to generate the design of

experiments. Each scenario provided 17 design points that were used to construct the

design surface using the Kriging methodology to predict the relationship between the

design variables and the response variable.

The three types of optimization used in ANSYS Workbench Goal Driven

Optimization are Screening, MORG, and NLPQL. The Screening approach is a non-

iterative direct sampling method by a quasi-random number generator based on the

Hammersley algorithm. The MOGA approach is an iterative Multi-Objective Genetic

Algorithm, which can optimize problems with continuous input parameters. NLPQL is a

78

gradient based single objective optimizer that is based on quasi-Newton methods

(ANSYS, 2009). Three different sets of initial points were used to ensure a global

optimal solution was achieved.

The Screening Optimization Method uses 10000 initial samples with a Constraint

Handing “As Goals” and a generated sample set of 1. This allows for the Objective in the

Optimization study of the deformation output parameter to be assigned as “Seek Target”

with a value of -3mm. The importance of this main objective is set to “higher”. This

technique results in three local optimal solution candidates as displayed in Table 14.

The MOGA Optimization Method also uses 10000 initial samples with a

Constraint Handing “As Goals” and a generated sample set of 1. In addition, there are

100 samples per iteration, a maximum allowable Pareto Percentage of 70 and a maximum

number of iteration of 50. The deformation response variable objective is set to “Seek

Target” with a value of -3mm and a higher importance. This technique also results in

three local optimal solution candidates as shown in Table 14.

Table 14: Optimal Design Variable Pressure Distributions and corresponding

deformation values from various Goal Driven Optimization Techniques

Optimization

Technique Deformation

(mm) Lateralheel Medialheel LateralMETS

Screening 1 -3.0002 0.14642 0.48862 0.11096

Screening 2 -2.999 0.14262 0.4389 0.16448

Screening 3 -3.0066 0.14137 0.36903 0.2356

MOGA 1 -3.0046 0.19372 0.32573 0.22655

MOGA 2 -2.9925 0.13672 0.33723 0.27204

MOGA 3 -2.9531 0.21571 0.30536 0.22493

NLPQL -3 0.28695 0.29992 0.15912

The NLPQL Optimization Method has an allowable convergence percentage of

1E-10, a maximum number of iterations of 50, and a generated sample set of 1. The

79

Constraint Handling is set to “As Goals” allowing the deformation objective to be set to

“Seek Target” with a value of -3mm and a higher importance. This particular technique

results in one global optimal solution as highlighted in Table 14.

The objective of this study was to show that as the plantar pressure distribution is

more specifically defined to an individual the closer the FEA deflection values match up

with the clinical deflection values as laid out in Table 13. The optimization feature was

utilized to find the optimal distribution by minimizing the error to zero and increasing the

P-value to 1 accepting the null hypothesis that the clinical data and FEA data are

equivalent as can be seen in Table 15.

Table 15: Uniform, 30/70 and Optimal Pressure FEA results compared to clinical data

(the deformations are in the negative z-direction)

Loading Orthotic

thickness Clinical deflection

accepted

FEA Model

deflection

measured

Percent

Error P-Value

t(mm) δ(mm) δ(mm) * **

Uniform 3.00 3.00 (0.25) 3.84 28.00 0.13

30/70 3.00 3.00 (0.25) 2.89 3.67 0.65

Optimal 3.00 3.00 (0.25) 3.00 0.00 1.00

* [(Accepted-Measured)/Accepted]x100

** H0: δclinical = δFEA vs. HA: δclinical ≠ δFEA

The optimal pressure distribution (Table 16) found in the optimization for the

medium subject can be considered a variation of Cavanaugh’s average distribution.

80

Table 16: Optimal Plantar pressure Distribution for medium subject.

Anatomic Region Pressure Distribution (%)

Medium Heel 29.99

Lateral Heel 28.7

Medial Mid-foot 1.4

Lateral Mid-foot 6.4

First Metatarsal 5.6

Second Metatarsal 8.4

Lateral Metatarsals 15.91

TOTAL 96.4

81

CHAPTER 6

SUMMARY & FUTURE WORK

Summary

These studies clearly indicate that modeling with FEA techniques offers a

consistent, accurate and reliable alternative to clinical studies, which contain many other

external uncontrollable factors, establishing a foundation for a methodical approach to

engineering modeling of orthotics. This approach offers a powerful framework to mimic

experimental and clinical study data and therefore can be a viable and valuable tool in the

custom design of orthotics based on individual’s unique needs and foot characteristics

without requiring extensive and expensive trial and error ad hoc approaches.

Each of the four surrogate modeling methods uses different algorithms to create a

surface, which describes the relationship between the input variables and the output data.

The Kriging method seems to have the ability to describe the custom foot orthotic

relationship the best for the purposes of this research. These Kriging surrogate models

are extremely efficient and accurate enough to be used in the custom foot orthotic

prescription process. The other methods are not advisable to be used for these purposes

and may be better suited for other relationships or situations with larger data sets.

Furthermore, these engineering models are easy and straightforward to modify for

specific use in practical situations. Such models can be flexible and adaptive to include

other design considerations, such as the activity factor, and foot deformities as seen in the

second case study. With the new and enhanced modeling capabilities, the CFO

prescriber can have the ability to be able to design and develop the best-fit CFO with the

optimal design characteristics for individual patients. Such a model could also enable

82

visual inspection of the impact of small changes in the input conditions on the overall

performance of the CFO.

Future work

These models open up a whole new world of studies to advance the knowledge

base on CFO’s. With these engineering models in conjunction with clinical trials many

developments can be made. Modeling is a tool that can greatly improve the methods that

are used to determine the effectiveness of orthotics. Some of the initial future research

may consist of: 1) running a more comprehensive clinical trial to gather more data on

specific groups to increase the accuracy of the FEA model. 2) Further investigate the

varying load distribution from the case study. Expand to include other subjects and

groups of people including obese populations which have been shown to carry their

weight very differently than “normal” populations. Also include a validation of the case

study by collecting the pressure distribution from the “medium” subject. 3) A clinical

study may also be run with only specific subject such as an “obese” group of subjects

collecting the pressure distribution between the foot and orthotic. This may be helpful

for both the first and second studies on this list. 4) Develop the Kriging surrogate models

in MATLAB in order to have use of equations. This may allow for more variability and

specification with the models including which correlation models to use. This may also

allow for the possibility of replacing the empirical table (Table 1) with the response

surface to include reference points for clinicians to easily reference. 5) Layer the FEA

model with soft nonlinear materials used in a full CFO. Including the soft materials will

create an even more accurate representation of the CFO behavior for future research and

design. 6) Investigate other stance phases such as heel strike and toe off.

83

APPENDIX

CLINICAL TRIAL DOCUMENTATION

84

ADULT INFORMED CONSENT DOCUMENT

University of Massachusetts

Amherst, MA 01003

Title: The validation of the design model of custom foot orthotics.

Principal Investigators: Lieselle Trinidad, MS; Sundar Krishnamurty, PhD; Ryan

Chang, MS; and Joseph Hamill, PhD.

Your written informed consent is required before you can participate in this project. Please read this document carefully and

then sign your name on the last page if you agree to participate. This document is in accordance with the Assurance of Compliance with the Office of Human Research Protection Regulations as approved by the Faculty Senate of the University of

Massachusetts.

Purpose: The purpose of this study is to validate the arch deflection of a design model

(FEA model) of a custom foot orthotic.

Eligibility: To participate in this study, you must be 10 to 60 years of age. You do not,

and have no history of: severe structural foot abnormality, arthritis, neurological

disorders, myopathies, cardiovascular disorder in the foot, foot infections and tumors.

Procedures:

This will be carried out at the University of Massachusetts, Biomechanics Laboratory

(Totman Building Room 23). You will complete a Modified Physical Activity Readiness

Questionnaire to determine your overall ability to participate in exercise. There will be a

total of two session to complete this study.

Session 1: We will measure your weight and end by making a cast of your foot from

which we will build a custom foot orthotic. This session will take approximately 30

minutes.

Session 2 (Motion Analysis Session): This will be carried out at the University of

Massachusetts, Biomechanics Laboratory. You will be asked to perform four tasks while

wearing the custom foot orthotics: 1) sit, 2) stand on one foot, 3) walk, and 4) run.

Before you begin any tasks, the custom foot orthotic will be taped to your bare skin and

reflective markers will be placed at three locations on the custom foot orthotic. The

movements of the reflective markers will be captured by cameras as you walk into their

recording area. After the orthotic and reflective markers are attached to your foot you will

sit on a chair with your foot placed on the force platform holding still for approximately

10 seconds, this is done to get a baseline reading of the arch height of the orthotic. This

task will be repeated 2-3 times. For the second task, you will be asked to stand on the

force platform on the one foot that has the orthotic attached to it. You will use a stick to

help you balance, and you will need to hold this position for about 10 seconds. That task

will be repeated 10 times. For the third and forth task you will be asked to walk then run

from one end of the laboratory to the other across the force platform making sure to place

85

the foot with the orthotic attached to it on the force platform. This will take

approximately 10 seconds and will be repeated 10 times for each activity. You will be

provided with rest periods as needed. At the end of the procedure, all markers will be

removed. Once you have completed all four tasks with the right foot we will ask you to

repeat the same sequence for the left foot. In total, this session should take approximately

90 minutes.

Possible Risks and Discomforts: The following risks and discomforts are associated

with the procedures described above.

Motion Analysis Session. During any type of exercise, there are slight possibilities of

health risks such as temporary fatigue and muscle soreness.

Confidentiality: Your identity and records will be kept confidential. While results from

this study will be shared with other researchers, no individual identities will be used in

any reports or publications resulting from this study.

In Case of Injury: In the unlikely event of injury resulting directly from participation in

this study, we will do everything we can to assist you in seeking medical treatment. The

University of Massachusetts will not provide compensation for medical treatment you

obtain.

Benefits: You will receive no direct benefit from participating in this study. Any

information that is obtained from this study will be made available to your physician,

upon request. The purpose of these studies is to provide the investigators with

information that will help us validate a design model of custom foot orthoses. This

information ultimately may have a positive impact on the research and development of

custom foot orthoses.

Costs and Reimbursement: No costs will be charged to you if you participate in this

study. You will receive one pair of foot orthoses after completing the study.

Withdrawal of Participation: Participation in this research is voluntary. You have the

right to withdraw from this study at any time.

Information: You are encouraged to ask questions about the study. The investigators

will attempt to answer all of your questions to the best of their knowledge. The

investigators fully intend to conduct the study with your best interest, safety and comfort

in mind. Please address any questions regarding the study Dr. Sundar Krishnamurty,

Ph.D. at [email protected], or to Lieselle Trinidad, M.S. (716) 310-7854. If you

would like to speak with someone not directly involved in the research study, you may

contact the Human Research Protection Office at the University of Massachusetts via

email at [email protected]; telephone (413) 545-3428; or mail at the Human

Research Protection Office, Research Administration Building, University of

Massachusetts Amherst, 70 Butterfield Terrace, Amherst, MA 01003-9242.



86

Participant’s Name Address

Signature Phone Number Date

______________________________

Investigator Signature

Department of Mechanical Engineering

87

MODIFIED PHYSICAL ACTIVITY READINESS QUESTIONAIRE

Initial Screening: Interview Date (MM/DD/YY):

______/______/______

Last Name _______________________ First Name ___________________________

Phone # Phone #

Email

Age (yrs) ______________ DOB: _____________________ Gender:

Female / Male

Height: _____ Feet, _____ Inches or ________ cm

Weight: ________________lbs or _________ kg

General health status _____________

Are you on medication?

Yes No Do you or have a significant past medical history? (eg. surgery, hospitalization )

__________________________________________________________

Yes No Any injuries in past the would affect walking?

Yes No Do you have physical limitations?

Yes No Do you have any heart problems?

Yes No Do you have diabetes?

Yes No Do you have arthritis?

Yes No Do you have neuropathies?

Yes No Circulations disorders? e.g. swelling of discoloration of your feet?

How did you hear about the study?__________________________________

88

Modified Physical Activity Readiness Questionnaire

1. Yes No Has your doctor ever said you had heart trouble or a heart murmur?

2. Yes No Do you ever suffer pains in your chest?

3. Yes No Do you ever feel faint or have spells of severe dizziness, passed

out, palpitations or rapid heart beat?

4. Yes No Has the doctor ever told you that your blood pressure was too high? (systolic >

160 mm Hg or diastolic > 90 mm Hg on at least 2 separate occasions)

5. Yes No Do you smoke cigarettes?

6. Yes No Do you have diabetes?

7. Yes No Do you have a family history of coronary or other atherosclerotic

disease in parents or siblings prior to age 55?

8. Yes No Has your serum cholesterol ever been elevated?

9. Yes No Is there any physical reason not mentioned here why you should

not follow an activity program even if you wanted to?

Below please provide an explanation for any of the questions to which you answered

YES.

________________________________________________________________________

________________________________________________________________________

____________________________________________________

Body Measurements

Height: _____ Feet, _____ Inches or ________ cm

Weight: ________________lbs or _________ kg

89

PARENTS INFORMED CONSENT DOCUMENT

University of Massachusetts

Amherst, MA 01003

Title: The validation of the design model of custom foot orthotics.

Principal Investigators: Lieselle Trinidad, MS; Sundar Krishnamurty, PhD; Ryan

Chang, MS; and Joseph Hamill, PhD.

Your written informed consent is required before your child can participate in this project. Please read this document carefully

and then sign your name on the last page if you agree to allow your child to participate. This document is in accordance with the Assurance of Compliance with the Office of Human Research Protection Regulations as approved by the Faculty Senate of the

University of Massachusetts.

Purpose: The purpose of this study is to validate the arch deflection of a design model

(FEA model) of a custom foot orthotic.

Eligibility: To participate in this study, participants must be 10 to 60 years of age.

Participant does not, and has no history of: severe structural foot abnormality, arthritis,

neurological disorders, myopathies, cardiovascular disorder in the foot, foot infections

and tumors.

Procedures:

This will be carried out at the University of Massachusetts, Biomechanics Laboratory

(Totman Building Room 23). Your child will complete a Modified Physical Activity

Readiness Questionnaire to determine his/her overall ability to participate in exercise.

There will be a total of two session to complete this study.

Session 1: We will measure your child’s weight and end by making a cast of his/her foot

from which we will build a custom foot orthotic. This session will take approximately 30

minutes.

Session 2 (Motion Analysis Session): This will be carried out at the University of

Massachusetts, Biomechanics Laboratory. Your child will be asked to perform four tasks

while wearing the custom foot orthotics: 1) sit, 2) stand on one foot, 3) walk, and 4) run.

Before your child begins any tasks, the custom foot orthotic will be taped to his/her bare

skin and reflective markers will be placed at three locations on the custom foot orthotic.

The movements of the reflective markers will be captured by cameras as your child walks

into their recording area. After the orthotic and reflective markers are attached to your

child’s foot your child will sit on a chair with his/her foot placed on the force platform

holding still for approximately 10 seconds, this is done to get a baseline reading of the

arch height of the orthotic. This task will be repeated 2-3 times. For the second task,

your child will be asked to stand on the force platform on the one foot that has the

orthotic attached to it. Your child will use a stick to help him/her balance, and he/she

will need to hold this position for about 10 seconds. That task will be repeated 10 times.

90

For the third and forth task your child will be asked to walk then run from one end of the

laboratory to the other across the force platform making sure to place the foot with the

orthotic attached to it on the force platform. This will take approximately 10 seconds and

will be repeated 10 times for each activity. Your child will be provided with rest periods

as needed. At the end of the procedure, all markers will be removed. Once your child

has completed all four tasks with the right foot we will ask him/her to repeat the same

sequence for the left foot. In total, this session should take approximately 90 minutes.

Possible Risks and Discomforts: The following risks and discomforts are associated

with the procedures described above.

Motion Analysis Session. During any type of exercise, there are slight possibilities of

health risks such as temporary fatigue and muscle soreness.

Confidentiality: Your child’s identity and records will be kept confidential. While

results from this study will be shared with other researchers, no individual identities will

be used in any reports or publications resulting from this study.

In Case of Injury: In the unlikely event of injury resulting directly from participation in

this study, we will do everything we can to assist your child in seeking medical treatment.

The University of Massachusetts will not provide compensation for medical treatment

your child obtains.

Benefits: Your child will receive no direct benefit from participating in this study. Any

information that is obtained from this study will be made available to your child’s

physician, upon request. The purpose of these studies is to provide the investigators with

information that will help us validate a design model of custom foot orthoses. This

information ultimately may have a positive impact on the research and development of

custom foot orthoses.

Costs and Reimbursement: No costs will be charged to you or your child if you

participate in this study. Your child will receive no reimbursement for participation in

this study.

Withdrawal of Participation: Participation in this research is voluntary. Your child has

the right to withdraw from this study at any time.

Information: You and your child are encouraged to ask questions about the study. The

investigators will attempt to answer all of your questions to the best of their knowledge.

The investigators fully intend to conduct the study with your child’s best interest, safety

and comfort in mind. Please address any questions regarding the study Dr. Sundar

Krishnamurty, Ph.D. at [email protected], or to Lieselle Trinidad, M.S. (716)

310-7854. If you would like to speak with someone not directly involved in the research

study, you may contact the Human Research Protection Office at the University of

Massachusetts via email at [email protected]; telephone (413) 545-3428; or



91

mail at the Human Research Protection Office, Research Administration Building,

University of Massachusetts Amherst, 70 Butterfield Terrace, Amherst, MA 01003-9242.

Participant’s Name Address

Parent/Guardian Signature Phone Number Date

______________________________

Investigator Signature

Department of Mechanical Engineering

92

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